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Abstract
In this study, we developed a novel planar bidirectional perfect metamaterial absorber (PMA) with polarization-selective absorption and reflection capabilities. The proposed bidirectional PMA has near-perfect absorption for y- and x-polarized waves propagating in the −z and + z directions. It also reflects x- and y-polarized waves propagating in the −z and + z directions. We used full-wave simulations and Fabry–Perot cavity models to evaluate the performance of the proposed bidirectional PMA. We also used a free-space method to measure the fabricated sample. To demonstrate the potential of the proposed PMA in multiband systems, we extended our PMA design to a dual-band bidirectional absorber.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Perfect metamaterial absorbers (PMAs) have attracted considerable scholarly attention because of their near-unity absorption [1–6], and their performance can be evaluated using equivalent circuit models [7,8]. Because their operating principle is based on mode resonance, PMAs can have an extremely thin structure [9–11]. Such absorbers can be used for solar energy capture [1] and infrared camouflage [2]. Other applications involve thermophotovoltaic cells [3] and the reduction of antennas’ radar cross-section [4]. In wireless communication, the avoidance of electromagnetic interference and coupling between antenna elements in the multiple-input multiple-output (MIMO) system is essential [12]. Moreover, interference between different wireless communication systems must also be minimized. Therefore, researchers have designed PMA structures that can suppress the electromagnetic interference of antennas [5,6].
Most absorber designs adopt the metal-insulator-metal configuration wherein a perfect electric conductor (PEC) ground plane is printed on the bottom layer. Such designs have one common drawback: They are only able to absorb an incident wave in one direction. This problem has been addressed in the literature. For example, an absorber design comprising two identical conductor patterns printed on different sides of the substrate has been proposed to utilize both electrical and magnetic resonance. It has the ability to absorb an incident plane wave regardless of its polarization and propagation direction [13–15]. To absorb an incident wave near unity, the resonant frequency of the electrical and magnetic resonance must overlap. The proposed absorber was capable of bidirectional wave absorption with polarization selectivity through the rotation of the conductor pattern printed on the bottom layer [16]. However, 10% of the incident power passed through the structure. The absorption performance was suboptimal because the chosen conductor pattern on the bottom of the absorber could not shield the transmitted wave completely. Huygens sources have been used as the meta-atom in the construction of a reference bidirectional absorber [17–21]. However, most Huygens sources are three-dimensional (3D) structures that are cumbersome and difficult to fabricate. Some researchers have proposed bidirectional PMA designs with a back-to-back configuration or 3D structure [22,23]. However, these designs do not have a low profile and might be difficult to implement.
Polarization-selective absorbers have considerable potential for use in various practical applications. In [24], a polarization-selective metamaterial absorber was used to reduce the radar cross section of an antenna array for incoming cross-polarized waves. However, because this absorber was almost transparent to the co-polarized signal, it did not influence the radiation performance of the array. In [25], a rasorber (radome + absorber) design inspired by the Great Wall of China was proposed. This rasorber exhibits polarization selectivity and reconfigurability and can be used in smart stealth systems. In [26], an absorber consisting of a metallic film and nanotrenches was developed to achieve high selectivity for p- and s-polarized waves and allow for the control and manipulation of light polarization. In [27], another absorber design with plasmonic grating and a dielectric–metal–dielectric multilayer was proposed for controlling the absorption rate on the basis of incident wave polarization. This absorber is suitable for use as a polarization detector and transmissive polarizer. In [28], a polarization-sensitive absorber consisting of graphene patches was developed. The proposed absorber has promising applications in polarization-sensitive filters and detectors. However, all of these aforementioned absorber designs [26–28] are capable of absorbing waves propagating in only a single direction. Therefore, a bidirectional absorber with polarization selectivity is required to enable novel applications in the field of light detection.
In [29], we developed a bidirectional absorber with polarization selectivity. We established a structure capable of bidirectionally absorbing x-polarized incident waves while allowing y-polarized waves to pass through, with absorption and transmission frequencies of 5.85 GHz. The proposed structure is composed of a cascaded ring-slot array printed on both sides of a dielectric substrate. We achieved polarization-selective and bidirectional properties by arranging the conductor pattern printed on the bottom layer in the same direction as the upper layer with a shift in the y-direction. However, despite its novel functionality, the proposed structure was limited to the bidirectional absorption and transmission of incident waves with the same polarization. Therefore, in this study, we developed a novel structure that can bidirectionally absorb and reflect incident waves with different polarization. The proposed bidirectional PMA can nearly perfectly (over 99%) absorb a y-polarized wave propagating in the −z direction and an x-polarized wave in the + z direction. Moreover, the proposed PMA also behaves as a perfectly electric conductor that can totally reflect x- and y-directional linear polarization waves in the −z and + z directions, respectively, in the whole operating band. We realized the unit cell of this novel PMA by printing a cascaded loop pattern on the top and bottom layers of the dielectric substrate and orienting the loop in the upper layer perpendicular to the loop in the lower layer. Unlike bidirectional absorbers comprising two conventional metamaterial absorbers in a back-to-back configuration [30], our structure contains only a single layer and maintains a low profile. The unit cell of our proposed structure is ultrathin. The thickness of the proposed absorber is only 1.6 mm, which is approximately 0.022λ (λ is the free-space wavelength of the absorption frequency). Full-wave simulations were conducted, and the results were verified using the Fabry–Perot cavity model [31,32] and the effective medium theorem [33–35]. The model and simulation results were highly consistent. To confirm the validity of the proposed design, we fabricated a 224 × 224 mm2 sample and measured its scattering coefficients in an anechoic chamber. The measured results were highly consistent with the simulation results. After achieving bidirectional absorption, we realized a novel bidirectional PMA design with two operating bands. The proposed PMA nearly perfectly (over 97%) absorbed the y- and x-polarized waves propagating in the −z-direction and + z-direction, respectively, at 4.32 and 5.27 GHz. Moreover, similar to a PEC reflector, the proposed PMA reflected the x- and y-polarized waves propagating in the −z-direction and + z-direction, respectively. Our PMA design enables new applications in many wireless communications systems. It can be used to enhance the performance of Fabry–Perot cavity antennas because of its capability to reflect co-polarized waves and absorb cross-polarized waves. The reflected waves meet the Fabry–Perot resonance condition and consequently produce a highly directed radiation beam. Unwanted cross-polarized waves are absorbed by the proposed PMA. It can also be used in the optical regime because its operating frequency can be tuned to the terahertz spectrum by scaling down its size. It can be used as a polarization detector or polarization-sensitive filter for light sensors. Because of its narrowband characteristic, it can be used as a sensitive detector, thermal imaging device, or thermophotovoltaic system [36]. In terahertz imaging systems, it can be used to selectively absorb incoming co-polarized waves. In such a scenario, the incident energy can be transformed into an infrared (IR) signal and detected by an IR camera [37].
2. Unit cell design
2.1 Geometry of the unit cell
The proposed absorber design is presented in Fig. 1. The full-wave simulator Ansys HFSS was used to simulate our structure. We assume that the cascaded loop array has infinite periods in our simulation. This assumption is satisfied by using the master–slave periodic boundary condition in the HFSS, which allows the array to extend infinitely on the x–y plane. We also used the Floquet port to periodically excite the structure in the simulation. The unit cell of the proposed absorber is depicted in Figs. 1(c)–(e). The conductor pattern was printed on an FR4 printed circuit board (ɛr = 4.4; loss tangent = 0.02) with a 1.6 mm thickness (approximately 0.022λ, where λ is the free-space wavelength of the absorption frequency). The thickness of the conductor layer was 0.035 mm. The coordinate system used in this paper was defined as in Fig. 1, and the origin was set to the center of the proposed absorber unit cell. The period of the unit cell in the x and y directions is px = py = 16 mm. The rest of the design parameters are presented in Table 1. Figure 1(c) illustrates the cascaded loop pattern printed on the top layer of the dielectric substrate. The loop element printed on the top layer connects to the neighboring element in the vertical direction, disconnecting from the neighboring element in the horizontal direction. This connection system interrupts the symmetry of the loop and increases the sensitivity to the polarization of the incident wave. The conductor patterns printed on the different sides are perpendicular to each other. The high polarization sensitivity achieved through this arrangement induces asymmetric absorption behavior.
Fig. 1. The proposed PMA. (a) Top layer and (b) bottom layer of the structure. (c) Top layer, (d) side view, and (e) 3D view of the unit cell.
Table 1. Detailed parameters of the unit cell.
2.2 Performance of the unit cell
The absorption rate was defined as follows: 1 − R(ω) − T(ω) = 1 − |S11|2 − |S21|2, where R(ω) = |S11|2 denotes the reflectivity, S11 denotes the reflection coefficient, T(ω) = |S21|2 denotes the transmissivity, and S21 denotes the transmission coefficient. The scattering and absorption performance of our proposed absorber was determined through full-wave simulation. Because of the geometric symmetry, we provide a description of the incident wave traveling only in the −z direction. We used the Ansys HFSS software package to simulate the scattering and absorption performance of the unit cell (Fig. 2).
Fig. 2. Frequency response of the proposed absorber. (a) Absorption rate and (b) scattering coefficients of y-directional polarization in the −z direction. (c) reflection of x-directional polarization in the −z direction, and (d) cross-polarization coupling in the −z direction.
The reflection coefficient is the total reflection coefficient as referred to for the remainder of this paper. As shown in Fig. 2(a), the proposed absorber absorbs y-directional linearly polarized waves propagating in the −z direction at 4.05 GHz, with an absorption rate near unity (over 99%). At the absorption frequency, the total reflection coefficient is low (i.e., < −25 dB), indicating that the electromagnetic energy of an incident wave can enter the structure without reflection loss, as shown in Fig. 2(b). We further compared this result with that of the x-directional linear polarization wave propagating in the −z direction, as presented in Fig. 2(c). The incident wave is polarized parallel to the long sections of the cascaded loop and can barely pass through the array (|S11| > −0.2 dB) in the frequency range of 0.5–18 GHz. According to the simulation results presented in Fig. 2(c), the performance of the proposed absorber is similar to that of a PEC plane over a large frequency range, and the incident wave is completely reflected when it is x-polarized. To verify that no scattering wave with cross-polarization is generated at the absorption frequency, we simulated the cross-polarization coupling and scattering of the unit cell, the results of which are depicted in Fig. 2(d). All terms are below −70 dB at the absorption frequency, confirming the absence of a cross-polarization coupling or scattering at the absorption frequency.
To examine the working principle underlying ultrawideband reflection, we modeled the cascaded loop pattern printed on the top layer as a dense mesh wire array for the x-polarized incident waves propagating in the −z-direction. We then determined the current distribution to visualize the physical mechanism of the dense mesh wire array. Figure 3 depicts the induced current on the loop pattern printed on the top layer. We assumed the incident wave was x-polarized, propagating along the -z-direction, and operated at 4.05 GHz. Our results indicate that the induced current was uniformly distributed and primarily oriented in the x-direction. Under these conditions, the surface behaved similarly to a PEC plane and reflected waves in a wide frequency range. The surface impedance of the dense mesh wire array (Zg) is expressed as follows [38]:
Fig. 3. Schematic of the induced uniform current for an x-polarized incident wave propagating in the −z-direction.
We conducted a full-wave simulation to determine the reflection coefficient of the structure. The simulated Гs value was −0.9994 + 0.0216j at 4.05 GHz, with the discrepancy (|Гt − Гs|/|Гs|) being only 0.29%. Therefore, we concluded that the cascade loop was equivalent to a dense mesh wire array, which is similar to a grating structure (which blocks light with polarization parallel to its orientation).
We investigated the performance of our structure under oblique incident waves. The wave impinges on the structure at incident angles θ of 0° – 60° in both the transverse electric (TE) and transverse magnetic (TM) polarization cases. The TE and TM incident waves are illustrated in Fig. 4, and the simulation results are displayed in Fig. 5. Figure 5(a) reveals that, under absorption mode for TE waves, the absorption frequency of the structure shifts to a higher frequency band as the incident angle increases, and the absorption rate decreases as the incident angle increases. The absorption frequency and absorption rate are 4.36 GHz and 93%, respectively, when the incident angle of the TE incident wave is 45°. Figure 5(b) reveals that the incident angle does not affect the performance of our structure in the TM polarization case, for which the structure acts as an absorber. The absorption frequency and the absorption rate are also shown to be nearly the same for all incident angles. These results imply that the proposed structure serving as an absorber is relatively insensitive to the incident angles of both TE and TM waves. To explain these simulation results, we refer to the literature [40,41]. According to [40], PMAs are insensitive to the incident angle of TM oblique waves because the magnetic field is always parallel to the surface of the substrate (xy plane). For TE waves, the absorption frequency increases primarily because the current path becomes shorter with oblique incidence [41]. In addition, absorption decreases because the magnetic field component transverse to the xy plane decreases as the incident angle increases [40]. To clarify the physical mechanism underlying this phenomenon, we discuss the magnetic flux formed by oblique incident waves. In TE incident waves, the normal component of the magnetic field is proportional to sin θ, where θ represents the incident angle. Consequently, as θ increases, the magnetic flux passing through the loop also increases. According to Lenz’s law, the magnetic flux created by a current induced on a loop tends to counteract changes in the external magnetic flux. Therefore, destructive interference occurs in the magnetic flux, and the inductance of the loop decreases. Consequently, the resonant frequency of the loop element and the absorption frequency of the PMA increase. Perfect absorption occurs only when the radiative damping rate matches the intrinsic damping rate [42,43]. However, for TE oblique incident waves, this rate balance is disrupted because the intrinsic damping rate is affected by ohmic loss, which changes as a result of the external magnetic flux, thereby leading to a decrease in the absorption rate. In cases involving the TM mode, the magnetic field vector is parallel to the surface on which the loop element is placed, regardless of the incident angle. Therefore, the resonant frequency of the loop remains constant, and the absorption frequency does not change with different incident angles. If our structure acts as a PEC reflector, its performance also does not vary with the incident angles [Figs. 5(c) and 5(d)]. The structure totally reflects the incident wave regardless of the incident angle. We conclude that our proposed structure has angular stability. Table 2 presents a comparison of the results obtained for the proposed absorber design and other published designs. The results indicate that the proposed absorber outperforms the majority of the other absorbers. It achieves bidirectional absorption with a near-unity absorption rate, polarization selectivity, high angular stability, and a low profile (with a thickness of 0.022λ). As presented in Table 2, none of the other absorbers can simultaneously achieve these properties. Therefore, our proposed PMA design is a valuable contribution to the research community.
Fig. 4. TE and TM incident waves. The structure acts as (a) an absorber and (b) a PEC reflector. (E: electric field; H: magnetic field).
Fig. 5. Frequency response for an oblique incident wave: absorption rate for a (a) y-polarized TE wave and (b) y-polarized TM wave and reflection coefficient (S11) for an (c) x-polarized TE wave and (d) x-polarized TM wave.
Table 2. Comparison of the proposed PMA with previously published bidirectional PMA designs.
3. Verification through full-wave simulation
We visualized the physical mechanism of the proposed absorber through full-wave simulation by using the Ansys HFSS software package. In the beginning, the incident wave was set as a y-directional linear polarization wave traveling in the −z direction (Fig. 1), and its operating frequency was set as 4.05 GHz. We adopted a logarithmic scale because the resulting field distribution can exhibit high contrast and high detail. The distribution of the electric (E) field in the dielectric substrate is displayed in Fig. 6. With reference to this figure, the absorption mechanism can be explained through the Fabry–Perot cavity model, whose resonance condition is that all the multiple reflections interfere constructively within the cavity. Our multilayer structure can be regarded as a metacavity with a high quality factor (Q). For additional details, please refer to Figs. S1–S4 and Eqs. (S1)–(S4) in Supplement 1. According to the Fabry–Perot cavity model [32], the standing wave induced in a cavity is attributable to the constructive interference occurring inside the dielectric layer, and this standing wave possesses a constant-phase property. The E-field magnitude distribution depicted in Fig. 6 indicates the presence of a standing wave bounded between the top and bottom layers and fluctuating in a similar manner to an LC oscillator. At different points inside the substrate, the induced fields are synchronized (without phase difference) and reach their peak magnitude at the same time. These phenomena suggest the presence of constructive interference and the absence of wave propagation. We thus inferred that the Fabry–Perot cavity model is suitable for describing the working principle of absorption.
Fig. 6. E field magnitude in the dielectric substrate: (a) t = 0, (b) t = T/12, (c) t = 2 T/12, (d) t = 3 T/12, (e) t = 4 T/12, (f) t = 5 T/12, and (g) t = 6 T/12, where T represents one period of oscillation.
Figure 7 displays a plot of the distribution of the magnetic (H) field in the dielectric substrate. As shown in Fig. 7, the mechanism underlying the proposed structure is similar to that underlying the Fabry–Perot cavity. A comparison of the figures reveals a quarter-cycle time difference between the E and H fields that corresponds to the 90° phase difference between these fields such that the Poynting vector of the field is purely imaginary. The standing wave inside the Fabry–Perot cavity is the reactive power corresponding to the purely imaginary Poynting vector and this quarter-cycle time difference. Notably, the electric field induced at the center of the x-directional line section is stronger than that at the end node of the section, which indicates that electrical energy is stored at the center. By contrast, magnetic energy accumulates at the node of the line section, as indicated in Fig. 7. A quarter-cycle time difference between the E and H fields implies that the electrical energy stored at the center of the loop section is converted into stored magnetic energy at the node of the loop section after a quarter period, and vice versa. Thus, the presence of LC oscillation within the substrate is confirmed by the field plot.
Fig. 7. H field magnitude in the dielectric substrate: (a) t = 0, (b) t = T/12, (c) t = 2 T/12, (d) t = 3 T/12, (e) t = 4 T/12, (f) t = 5 T/12, and (g) t = 6 T/12, where T represents one time period of oscillation.
4. Methods and discussion
We used a Fabry–Perot cavity model [31,32] to examine the wave absorption performance of the proposed PMA. For more details about this model, please refer to Figs. S1–S6 and Eqs. (S1)–(S9) in Supplement 1. Figure 8 shows a plot of the frequency response of the absorption rate according to the Fabry–Perot cavity model. We assumed a y-polarized incident wave propagating in the −z direction. As shown in Fig. 8(a), we calculated the absorption frequency as 3.91 GHz, with a corresponding absorption rate of 99.1%. The curve shown in Fig. 8(a) is relatively consistent with that shown in Fig. 2(a). The difference between the absorption frequencies as depicted in Figs. 2(a) and 8(a) is only 0.14 GHz, representing a discrepancy of only 3.5%. This small discrepancy may be due to the omission of the electromagnetic coupling and interaction between layers in the Fabry–Perot cavity model. The coupled resonance between structures might influence the scattering response of the proposed PMA [47,48]. However, we used a transfer matrix method that excluded electromagnetic coupling as a mathematical tool for Fabry–Perot cavity model analysis. Moreover, in the Fabry–Perot cavity model, the thickness of the cascaded loop pattern is assumed to be zero, but the practical conductor layer must have a finite thickness. Figure 8(b) presents all the absorption rates obtained from the full-wave simulation and Fabry–Perot cavity model in a single plot. Despite the small discrepancy, the trends of the two dispersive curves are consistent. Therefore, our proposed absorber can be treated as a metacavity with a high quality factor (Q).
Fig. 8. Calculated absorption rate. (a) Absorption rate plotted using the Fabry–Perot cavity model. (b) Comparison of the simulation and model results.
We investigated the absorption mechanism by using the effective medium theorem [33,34]. For more details about this theorem, please refer to Fig. S7 and Eqs. (S10)–(S14) in Supplement 1. We used the effective impedance Z (normalized to the intrinsic impedance Z0) and refractive index n to characterize the proposed absorber. Figure 9 presents the Z and n values of the proposed absorber for a y-polarized incident wave propagating in the −z direction. The real part of Z approaches one, and the imaginary part of Z is approximately zero at the absorption frequency of 4.05 GHz. These results indicate that the impedance matching condition is satisfied at the absorption frequency. The imaginary part of n is −19.24 at the absorption frequency. This negative value indicates that the strength of a transmitted wave drastically decays while passing through the absorber.
Fig. 9. Effective parameters of the proposed absorber for a y-polarized wave: (a) impedance Z and (b) refractive index n.
We examined the effective n and Z values for an x-polarized incident wave propagating in the −z-direction. Figure 10 lists the frequency responses. Both the real and imaginary parts of Z are close to 0 in the entire observation band. Moreover, the real part of Z is approximately 17 times smaller than the imaginary part of Z at 4.05 GHz. These results imply that the absorber behaves like a PEC reflector whose impedance is an inductor with a small value in the lower band. The imaginary part of n is −2.29 at the absorption frequency, indicating little transmission of the incident wave through the structure. As indicated by Figs. 10(a) and 10(b), if the incident wave is an x-directional linearly polarized wave, then most energy of this wave is reflected by the proposed PMA. This conclusion is consistent with the simulation results depicted in Fig. 2(c).
Fig. 10. Effective parameters of the proposed absorber for an x-polarized wave: (a) impedance Z and (b) refractive index n.
5. Frequency scalability of the proposed PMA
Because of the resonant nature of the proposed PMA, we assumed that its physical dimensions were proportional to its operating wavelength and that we could thus adjust the operating frequency to the terahertz band by decreasing the absorber’s physical dimensions. To validate our assumption, we set the operating frequency to 2 THz and reengineered our PMA. Because FR4 has low performance in the terahertz band, we replaced it with SiO2 (permittivity = 3.5) as the dielectric substrate. We also used silver (conductivity = 6.3 × 107 S/m) for the printed conductor layer. Because silver is dispersive, we considered its permittivity to be (1.77 × 3.87i) × 105 at 2 THz [49].
The original PMA operates at a wavelength of λ1 = 3 × 108/(2.7)0.5 × (4.05 × 109)−1, but the redesigned structure was to operate at a wavelength of λ2 = 3 × 108/(2.25)0.5 × (2 × 1012)−1, with 2.25 being the average relative permittivity of vacuum and SiO2. We scaled down all the geometric parameters of the structure by a factor of λ2/λ1. We also fine-tuned the structure to increase its absorption rate. Consequently, we realized a PMA capable of operating at 2.01 THz with an absorption rate of 99.1%. Figure 11 depicts the geometry of the unit cell, and Fig. 12 summarizes its performance. The design parameters shown in Fig. 11 are detailed in Table 3. In summary, we shifted the operating frequency of the proposed PMA by scaling down its physical dimensions and fine-tuning its structure, with the main limitation being the necessary nanofabrication technology.
Fig. 12. Frequency response of the redesigned absorber for use in the terahertz band: (a) absorption rate of y-directional polarization in the −z direction and (b) reflection of x-directional polarization in the −z direction.
Table 3. Detailed parameters of the modified unit cell.
6. Measurement results
We employed the free-space method to measure the reflection and transmission coefficients to verify the proposed PMA design. The experiment was conducted in an anechoic chamber. Figure 13 depicts the fabricated sample and measurement setup. The sample size was 224 × 224 mm2, comprising 14 × 14 unit cells. The conductor patterns were printed on the substrate, which comprised an FR4 membrane with a thickness of 1.6 mm and a relative permittivity of 4.4. To measure the reflection and transmission coefficients, the device under test (DUT) and standard horn antenna were positioned 1 m apart. Thus, the distance between the two standard horns was 2 m when the transmission coefficients were measured. The standard horn antennas were connected to the Agilent E5071c ENA network analyzer. When measuring reflection, we used the reflection of the metal plane (224 × 224 mm2) to calibrate the reflection coefficient. The two standard horn antennas were placed side by side, with their middle point aligned with the center of the DUT. The two standard horns were placed as close as possible to obtain measurements at normal incidence. When the transmission was measured, the received signal transmitted through the direct free-space path was used as a reference; the two horn antennas were placed on each side of the sample.
Fig. 13. Fabricated structure and measurement environment. (a) Implemented sample; (b) S11 and (c) S21 measurement.
Because the proposed PMA is symmetric, we only considered the wave propagating in the z direction. A comparison between the simulated and measured results is presented in Fig. 14. The figure demonstrates that the simulated results agreed with the measured results. The data indicated a frequency discrepancy of only 0.02 GHz between the measured and simulated results. The slight discrepancy observed in the measured signal may be due to fabrication error and the finite size of the sample. Nevertheless, the measured results provide sufficient validation of our design.
Fig. 14. Comparison of the simulated and measured results. (a) Absorption rate of the x-polarized wave; (b) scattering coefficients of the x-polarized wave; and (c) reflection coefficient of the y-polarized wave.
7. Parametric study
We varied the substrate thickness and loop circumference to investigate how these physical dimensions affect the absorption performance of the proposed PMA. The incident wave exhibited y polarization and propagated in the −z direction. The results are presented in Figs. 15 and 16. As shown in Fig. 15, the absorption frequency decreased when the thickness of the substrate was increased. The absorption rate also decreased when the thickness deviated from the optimal value of 1.6 mm. As depicted in Fig. 16, when the circumference increased, the absorption frequency decreased. Overall, the simulation results indicate that the performance of the proposed PMA is closely linked to the thickness of the substrate and the circumference of the loop. These results are further discussed in Supplement 1. For more details, please refer to Eq. (S1) and Figs. S8 and S9.
8. Dual-band bidirectional absorber
Our bidirectional absorber can be extended to have dual operating bands. We added two small loops to the unit cell to introduce an additional absorption frequency. The resulting structure is displayed in Fig. 17, the design parameters of the dual-band device are presented in Table 4, and the frequency responses are depicted in Fig. 18. As shown in Fig. 18, the novel dual-band absorber design can absorb y- and x-polarized waves propagating in the −z-direction and + z-direction at two distinct frequencies, with the absorption rate exceeding 97% at 4.32 and 5.27 GHz. The proposed design also reflects x- and y-polarized waves propagating in the −z-direction and + z-direction similarly to how a PEC reflector does. The reflection coefficient of our design is close to 0 dB in the entire operating band in this situation.
Fig. 17. Dual-band bidirectional absorber: (a) top layer and (b) bottom layer of the structure; (c) top layer, (d) side view, and (e) 3D view of the unit cell.
Fig. 18. Frequency response of the dual-band bidirectional absorber: (a) absorption rate of y-directional polarization waves in the −z-direction and (b) reflection coefficients (S11) of x-directional polarization waves in the −z-direction.
Table 4. Detailed parameters of the bidirectional dual-band PMA design.
Overall, our findings provide preliminary evidence that our proposed bidirectional absorber can be redesigned to have two distinct operating bands. In the future, we intend to further improve the bandwidth of our dual-band bidirectional absorber and conduct comprehensive investigations on the new design. We also intend to develop a bidirectional absorber with more than two operating bands on the basis of the design proposed in this paper.
9. Conclusion
In this study, we proposed a novel bidirectional absorber design that can absorb y- and x-directional linear polarization waves traveling in the −z and + z directions, respectively. The proposed PMA also serves as a perfect electric conductor that can completely reflect x-directional and y-directional linearly polarized waves in the −z and + z directions over a large frequency range (0.5–18 GHz). The proposed PMA has a single-layer structure with a cascaded loop array printed on both sides of a substrate. This PMA design is ultrathin (with a thickness of only 0.022λ) and is easier to fabricate than multilayer structures. Asymmetric absorption behavior with a near-unity absorption rate can be achieved by rotating the pattern printed on the bottom layer and fabricating it perpendicular to the pattern printed on the top layer. This unique polarization selectivity is suitable for Fabry–Perot resonant cavity antennas; the bidirectional absorption and reflection characteristics can enable bidirectional radiation by such antennas. The Fabry–Perot cavity model and the effective medium theorem were employed to analyze the working mechanism of the bidirectional PMA. The characteristic features of the absorber were well explained by these models, and results from the theoretical analysis and full-wave simulation were highly consistent. In addition, we fabricated and measured the proposed PMA design. The simulated results were well reproduced, which validated the performance of the PMA. Furthermore, we amended the original bidirectional absorber to have dual operating bands, and the simulation results indicate that our novel bidirectional PMA can be easily extended to a dual-band bidirectional PMA. We provide a novel bidirectional absorber design. Our proposed structure and design procedure may offer other researchers a new means of realizing bidirectional absorbers.
Acknowledgments
This work was partially funded by the National Science and Technology Council (NSTC) of Taiwan under Grant numbers NSTC 112-2221-E-A49-067. We appreciate the assistance from Prof. Yu-Min Lee in our department for using the Ansoft HFSS software. We would like to thank Prof. Chao-Shun Yang and Zi-Meng Zhuang for their technical assistance with experimental measurements. We would also like to thank Ming Chi University of Technology for providing the experimental equipment.
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.
Supplemental document
See Supplement 1 for supporting content.
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