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Abstract
In this study, we developed a novel planar bidirectional perfect metamaterial absorber (PMA) with polarization-selective absorption and transmission capabilities. The proposed structure can bidirectionally absorb x-polarized incident waves almost perfectly while functioning as a transparent surface for y-polarized incident waves at the same frequency. We discussed the performance and properties of the proposed PMA through simulation results and a theoretical model. We also used the free-space method in experimental tests of a fabricated sample. The results indicated fair consistency between the simulated and measured results, thereby validating the quality of our PMA design.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metamaterials are artificial structures with unique electromagnetic characteristics and can be realized using two-dimensional (2D) [1,2], three-dimensional (3D) [3,4], and quantum [5–7] materials. Because 2D metamaterials are usually much lighter and thinner than their 3D counterparts and are easy to fabricate, we focused on 2D metamaterials in this study. Tuning metamaterials can be used in a variety of applications when their properties are tuned accordingly. For example, metamaterials can be used to manipulate light polarization [8] or as media with high refractive indices [9]. They can also be used to realize planar structures with multiple tunable plasmon-induced transparency windows [10]. Among the various potential applications of metamaterials, perfect metamaterial absorbers (PMAs) have attracted considerable research attention. PMAs can operate in the microwave [11], infrared [12], and ultraviolet [13] spectra. They can be used in applications involving selective thermal emission [14], refractive index sensing [15,16], biomedical sensing [17], infrared camouflaging [18], thermophotovoltaic cells [19], and radar cross section (RCS) reduction in antennas [20–22]. To date, various PMA designs have been proposed with ultrawideband [23] and polarization-insensitive [24] characteristics. However, most absorber designs include a ground plane composed of a near-perfect electric conductor, which can block transmitted waves. This plane also reflects the waves incident on it. Therefore, such absorbers cannot absorb incident waves in both directions.
Several researchers have attempted to design bidirectional absorbers. For example, absorber designs with two identical conductor patterns printed on different sides of a substrate have been proposed [25–29]. Although such structures can absorb incident waves regardless of their polarization and propagation directions, they cannot switch between operating modes. An absorber composed of multiple thin films and a nanocube array was proposed [30]. This absorber includes multiple conductor and dielectric slabs, with the nanocube array installed on top. The structure successfully absorbs incident waves across a wide frequency range in one propagation direction and absorbs waves in two narrow bands in the other propagation direction. However, the multilayer structure of this absorber is difficult to fabricate, hindering its potential applications. Several proposed bilayer structures can transform an incident wave into an evanescent wave [31,32]. These absorbers’ unit cells can bidirectionally absorb incident waves with specific polarization and reflect those with another polarization. However, reflected waves can cause communication blockades in wireless communication systems and result in an undesired increase in the RCS of the antenna [33].
PMAs that can bidirectionally absorb or transmit incident waves on the basis of polarization are in high demand. In wireless communication systems, these devices can function as spatial filters to suppress unwanted cross-polarized waves while allowing co-polarized waves to pass through. This capability is useful for full-duplex communication systems, because signals can be transmitted in both directions simultaneously. However, cross-polarized noise must be attenuated from each side of the PMA. PMA designs with selective wave absorption and transmission capabilities have the potential to be used in wireless-powered communication networks (WPCNs) [34,35]. In a WPCN, energy-harvesting technologies can be integrated into a communication system. PMAs with polarization-selective capabilities can be used to efficiently capture wireless power from cross-polarized noise without compromising the quality of the wireless communication system. They can also be used as transverse magnetic (TM) polarization filters with a high extinction ratio by absorbing unwanted transverse electric (TE) polarized waves. These TM polarization filters are crucial for level-free sensing [36] and polarization multiplexing [37]. Devices that can provide a high extinction ratio with no increase in the insertion loss of the TM mode are desirable for these applications.
Recently, a structure called a frequency-selective rasorber (FSR) was proposed. This structure consists of a lossless frequency-selective surface and a lossy layer, and it allows in-band signals to pass through it while absorbing out-of-band signals [38]. Several studies have focused on the design of FSRs. For example, an FSR with a tunable transmission window was proposed [39]. The transmission window within the absorption band could be tuned by varying the capacitance of the loading varactors, and the insertion loss of the transmitted signal was 0.59 dB. However, the realized FSR had a three-layer structure with a total thickness of 14.6 mm. In the reference, an FSR with favorable angular stability was proposed [40]. This FSR performed well for incident angles up to 45°, and the insertion loss was only 0.44 dB. However, the structure was also composed of three layers with a total thickness of 10.1 mm. An FSR with a one-layer structure and a total thickness of 0.254 mm was proposed [33]. This FSR had two pass bands and three absorption bands, with absorption rates of 94%, 96.81%, and 91.91% at 6.6, 11.1, and 14.7 GHz, respectively. The passbands of this structure were at 9.6 and 13.4 GHz, with insertion losses of 0.3 and 0.5 dB, respectively. Notably, none of the currently available FSRs can operate bidirectionally [33,38–40], and their transmission and absorption frequencies cannot be the same. Therefore, these structures are considered to be different from the PMA proposed herein.
We propose a novel planar structure that behaves similarly to a bidirectional absorber (with an absorption rate higher than 97.1%) for x-polarized incident waves. The proposed structure can successfully switch to transmission mode when the incident wave is y-directionally polarized, with a transmission coefficient S21 (S12) of −0.311 dB, which is superior to the insertion losses of the FSRs proposed in [38–40] and is close to the insertion loss of the FSR proposed in the Ref. [33]. The absorption frequency of the x-polarized incident wave is 5.85 GHz, which coincides with the transmission frequency of the y-polarized incident wave. Compared with the FSR designs proposed in [33,38–40], our design is more suitable for level-free sensing [36], polarization multiplexing [37], and polarization filtering in communication systems because it can differentiate waves with different polarization at the same frequency. Functioning as both a bidirectional absorber and a transparent surface, the proposed structure is angular stable and performs well (with an absorption rate higher than 93% and an insertion loss lower than 0.55 dB) when the incident angle does not exceed 45°. The unit cell has a cascaded ring-slot pattern printed on the top and bottom surfaces of a dielectric substrate with a relative displacement of 6.2 mm in the y-direction between the patterns on each side. Unlike the 3D structures developed in [38–40], our unit cell has a low profile. Our novel PMA design also has considerable potential in many applications, such as in full-duplex communication systems, WPCNs, level-free sensing, and polarization multiplexing. We validated the performance of our design using full-wave simulations. We also compared our structure against its counterparts in the literature (Section 3.1). Subsequently, we used the effective medium theorem [41–43] to verify the impedance matching of the proposed structure. We also analyzed the distribution of the electric field (E-field) to determine the physical mechanism underlying the functionality of the proposed bidirectional PMA in Section 3.3. The results indicated that the absorption of the x-polarized incident waves was linked to the formation of standing waves in the transverse direction. We also observed a uniform magnetic current on the surface for a y-polarized wave passing through the structure. To demonstrate the validity of the proposed design, we fabricated a 224 × 224 mm2 sample and measured its scattering parameters using the free-space method. The simulation results agreed with the empirical measurements very well.
2. Unit cell design
Figure 1 shows the proposed PMA. The conductor pattern is printed on an FR4 printed circuit board (εr = 4.4, loss tangent = 0.02) with a conductor layer thickness of 0.035 mm. Notably, the loss component of relative permittivity (loss tangent) plays a major role in the design of the PMA because it can be used to induce high absorption [44]. The loss tangent is closely related to the intrinsic damping rate. Perfect absorption is attained when the radiative damping rate matches the intrinsic damping rate [45,46]. The radiative damping rate can be adjusted by altering the thickness of the substrate [46]. Therefore, to achieve near-unity absorption, we optimized the thickness of the substrate. Through multiple optimizations, we discovered that the total thickness of the FR4 substrate should be 0.8 mm (approximately 0.016λ, where λ is the free-space wavelength of the absorption frequency). The period L of the unit cell is 16 mm. The unit cell of the proposed absorber is presented in Figs. 1(d)–1(g), and the design parameters of the unit cell are detailed in Table 1. The ring slot pattern printed on the top and bottom surfaces of the dielectric substrate is presented in Figs. 1(d) and 1(e). The ring slot in each unit cell is vertically cascaded to the neighboring slot element, and the patterns printed on the different sides are set apart from each other by 6.2 mm in the y-direction (shifty). The connection between the ring-slot elements generates an induced uniform magnetic current for y-polarized incident waves; the separation between the patterns on the opposite sides creates standing waves along the transverse direction in response to x-polarized incident waves. Overall, this PMA design offers different functionality based on polarization.
Fig. 1. The proposed PMA. (a) Top layer, (b) bottom layer, and (c) 3D view of the structure. (d) Top layer, (e) bottom layer, (f) side view, and (g) 3D view of the unit cell.
Table 1. Detailed unit cell parameters.
3. Method and results
3.1 Performance of the unit cell
We used a full-wave high-frequency structure simulator (HFSS) to simulate our structure. However, because the ring slot array was considered to have an infinite period, we used a master–slave periodic boundary condition along the xy direction. The E-field at every point on the slave boundary surface is forced to match the E-field of the corresponding point on the master boundary surface. Consequently, the master and slave boundaries mimicked the infinite extension of the PMA in the xy plane. To excite our PMA, we imposed Floquet ports along the z-axis. Floquet ports are closely related to the set of plane wave modes, with the propagation direction set by the geometry of the periodic structure. When Floquet ports are used along the z-axis, space boundary conditions need not be considered. We defined the absorption rate as 1 − R(ω) − T (ω) = 1 − |S11|2 − |S21|2, where R(ω) = |S11|2 is the reflectivity, S11 is the reflection coefficient, T(ω) = |S21|2 is the transmissivity, and S21 is the transmission coefficient. Next, we used the HFSS commercial software package to simulate the scattering and absorption performance of the unit cell. The simulation results are presented in Fig. 2 (the reflection coefficient shown in Fig. 2 is hereinafter used as the total reflection coefficient). The proposed structure successfully absorbed x-polarized linear waves propagating in the −z- and + z-directions at 5.85 GHz at a rate higher than 97.1%. In addition, as shown in Figs. 2(c) and 2(d), the total reflection coefficient was low (5.85 GHz). These results indicate that incident electromagnetic energy can fully enter the structure without reflection loss. For comparison, we considered a y-polarized incident wave. As shown in Figs. 2(e) and 2(f), a y-polarized wave propagating in the + z- and −z-directions could pass through the whole structure. In addition, the transmission coefficient was −0.311 dB, whereas the reflection loss was less than 12.3 dB. Therefore, the proposed PMA can be used to absorb noise with cross-polarization while reserving the propagation channel for signals with co-polarization. As a next step, we simulated the performance of the proposed PMA with an oblique incident wave. The simulation setup is presented in Fig. 3, and the results are outlined in Fig. 4. As shown in Figs. 4(a) and 4(b), the absorption rate did not considerably change with the incident angle of oblique TM waves and was 95.57% at an incident angle of 45°. However, it decreased as the incident angle increased for oblique TE incident waves. For TE waves, the PMA maintained a high absorption rate (93.53%) for incident angles up to 45°. As shown in Figs. 4(c) and 4(d), the transmission coefficient S21 of the proposed PMA increased as the incident angle increased for TM incident waves. In addition, the insertion loss of the transmitted signal was only 0.145 dB at an incident angle of 45°. However, for TE waves, the insertion loss S21 was not sensitive to the incident angle. In other words, it remained 0.541 dB at an incident angle of 45°. These results indicate that the proposed structure exhibits angular stability and outstanding performance, even for waves at an incident angle of 45°. Table 2 compares the proposed absorber with other previously published designs.
Fig. 2. Frequency response of the proposed absorber. Absorption rate of the x-polarized wave propagating in the (a) −z-direction and (b) +z-direction. Scattering coefficients of the x-polarized wave propagating in the (c) −z-direction and (d) +z-direction. Scattering coefficients of the y-polarized wave propagating in the (e) −z-direction and (f) +z-direction.
Fig. 3. Simulation setup. (a) x-polarization, (b) y-polarization (E: electric field, H: magnetic field).
Fig. 4. Frequency response of an oblique incident wave. Absorption rate for an (a) x-polarized TE wave and (b) x-polarized TM wave. Transmission coefficient (S21) for a (c) y-polarized TE wave and (b) y-polarized TM wave.
Table 2. Comparison of the proposed PMA with other publised designs.
3.2 Effective medium theorem
In this section, we assume that the incident wave propagates in the −z-direction. In accordance with [41–43], we modeled a planar structure as a dielectric medium with effective impedance Z (normalized to intrinsic impedance Z0) and refractive index n. We then calculated the values of Z and n for the proposed absorber by using the methods proposed in [41,42]. In the following equations, d denotes the thickness of the absorber and m is an arbitrary integer:
To select a proper value for m, we used the Kramers–Kronig relations [43] as follows:
Because uniform dielectric slabs can be treated as transmission line sections, we calculated the input impedance of the absorber as follows:
Subsequently, we derived the values of Z and n from Eqs. (1) and (2) and examined the input impedance (normalized to Z0) of the proposed absorber through Eq. (6). Figure 5 depicts the input impedance of the proposed structure.
Fig. 5. Input impedance for the (a) x- and (b) y-polarized waves. The incident wave is propagating in the −z-direction.
We used the following equation to calculate the reflection coefficient S11: 20 × log10(|(Zin − 1)/(Zin + 1)|) (dB). Using Zin derived from Eq. (6), we obtained S11 values of −29.47 and −12.35 dB for x and y polarization, respectively, at 5.85 GHz. These results strongly agree with the full-wave simulation results depicted in Fig. 2. They also indicate that the proposed structure achieves impedance matching (S11 < −10 dB) for both polarization types
3.3 E-field distribution
We used E-field distribution to visualize the physical mechanism of the proposed structure. To present the field distribution along neighboring unit cells, we plotted the E-field intensity of two contiguous unit cells. We first considered an x-polarized incident wave propagating in the −z-direction and then observed the x component of the electric field (Ex) on the side plane at a specific absorption frequency. The simulation setup is depicted in Fig. 6, and the Ex distribution on the side plane is presented in Fig. 7. As shown in Fig. 7, the field intensity on the bottom surface varied in the y-direction. Figure 8 shows a plot of the Ex distribution on the bottom surface; the standing waves formed in the y-direction. We observed that Ex switched to the opposite direction every half-period. Because we used a rectangular lattice design, we compared the field distribution with a sinusoidal (trigonometric) distribution. The comparison revealed the accumulated phase delay of a standing wave in the y-direction to be 2π. Therefore, the y-component of the k vector was 2π/L = 392.7 for a surface wave, where L (16 mm) denotes the period of the array. The wavenumber in vacuum (k) was equal to ω/Vp = 122.5, where Vp is the phase velocity of light in vacuum. In this scenario, k was much smaller than ky, indicating that the surface waves on our device decay exponentially in the z-direction [31]. We illustrate the standing wave distribution in the y-direction in Fig. 9.
Fig. 6. Simulation setup for field distribution on the side plane. (a) Side view of the simulation setup. (b) 3D view of the simulation setup.
Fig. 7. Ex amplitude distribution on the side plane of two neighboring cells for an x-polarized incident wave propagating in the -z-direction. (a) t = 0, (b) t = T/16, (c) t = 2 T/16, (d) t = 3 T/16, (e) t = 4 T/16, (f) t = 5 T/16, (g) t = 6 T/16, (h) t = 7 T/16, and (i) t = 8 T/16, where T denotes one period of oscillation.
Fig. 8. Ex amplitude distribution on the bottom surface of two neighboring cells for an x-polarized incident wave propagating in the −z-direction (each orange rectangle represents a copper line): (a) t = 0, (b) t = T/16, (c) t = 2 T/16, (d) t = 3 T/16, (e) t = 4 T/16, (f) t = 5 T/16, (g) t = 6 T/16, (h) t = 7 T/16, and (i) t = 8 T/16, where T denotes a single oscillation period.
Fig. 9. Standing wave distribution along the y-direction (each orange rectangle represents a copper line).
Generally, the bottom surface can satisfy the transverse resonance condition if it has a standing wave [50] (further discussion in the appendix); the bottom surface can be modeled as a resonant cavity in the presence of a standing wave. In our case, the equivalent circuit of the ring slot was a parallel LC resonator. When the circumference of the ring slot was equal to one wavelength, the ring slot was resonant, and the standing wave was on the bottom surface (along with the slot). The induced standing wave distribution along the ring slot is illustrated in Fig. 10. To determine the effective circumference of the ring slot, we plotted the Ey distribution on the bottom surface (Fig. 11). Figures 8 and 11 depict a standing wave on the ring slot. Using the field distribution shown in these figures, we calculated the effective side length of the ring slot. The results indicated that the effective side length in the x-direction was equal to the length of the cut wire (14.05 mm), whereas the effective side length in the y-direction was equal to w1 + 0.5 × gap1 + 0.5 × gap2 (1.8 mm). The symbols used in this study are defined in Fig. 1, and their values are listed in Table 1. The method we used to calculate the effective side length is presented in Fig. 12.
Fig. 11. Ey amplitude distribution on the bottom surface of two neighboring cells for an x-polarized incident wave propagating in the −z-direction (each orange rectangle represents a copper line): (a) t = 0, (b) t = T/16, (c) t = 2 T/16, (d) t = 3 T/16, (e) t = 4 T/16, (f) t = 5 T/16, (g) t = 6 T/16, (h) t = 7 T/16, and (i) t = 8 T/16, where T denotes a single oscillation period.
Fig. 12. Schematic of effective side length calculations. (a) y-direction, based on Fig. 8; (b) x-direction, based on Fig. 11.
By summing the effective side lengths in the x- and y-directions, we calculated the effective circumference of the ring slot to be 31.7 mm and the phase velocity of the wave to be 3 × 108/(εr)0.5 = 3 × 108/(2.7)0.5, where εr is the average of the relative permittivity of vacuum and FR4. The calculated resonant frequency was 5.76 GHz, which is close to the absorption frequency (5.85 GHz) obtained from the full-wave simulation, confirming that the wave absorption was due to the induced surface wave.
To explain the physical mechanism of absorption, we investigated the surface current distribution on the bottom surface. Figure 13 depicts the distribution of current. As shown in Figs. 8–11 and 13, the current and E-field distributions were similar in some respects but different in others. The current vector induced on the cut wire switched to the opposite direction every half-period, indicating the presence of a standing wave in the y-direction (also shown in the E-field distribution, Fig. 9). However, the current was aggregated at the center of the conducting wire, which differed from the E-field distribution. This phenomenon was also observed in the LC resonator. Thus, we confirmed the presence of a standing wave on the resonant ring slot.
Fig. 13. Current distribution on the bottom surface for an x-polarized incident wave (each orange rectangle represents a copper line; the arrows represent the flow direction of current).
We next considered a y-polarized incident wave propagating in the −z-direction and observed the Ey distribution on the bottom surface. The field distribution and induced magnetic current are presented in Fig. 14, and the simulation results are plotted in Fig. 15. The distribution of the Ey value on the bottom surface had no phase delay in the y-direction, as indicated in Fig. 15. In addition, the electric field on the slot was mainly oriented in the y-direction and was uniform in the x-direction. According to the surface equivalence principle, Ey is equivalent to the magnetic current in the x-direction. This confirms that the magnetic current is uniform on the ring slot when a y-polarized wave is incident on the structure and that the surface in such a situation is transparent for the incident wave.
Fig. 14. Schematic of the induced uniform magnetic current (two cells in the x-direction) for a y-polarized incident wave propagating in the −z-direction (each orange rectangle represents a copper line).
Fig. 15. Ey amplitude distribution on the bottom surface for a y-polarized incident wave propagating in the −z-direction (each orange rectangle represents a copper line): (a) t = 0, (b) t = T/16, (c) t = 2 T/16, (d) t = 3 T/16, (e) t = 4 T/16, (f) t = 5 T/16, (g) t = 6 T/16, (h) t = 7 T/16, and (i) t = 8 T/16, where T denotes a single oscillation period.
To further uncover the mechanism of wave transmission, we examined the current distribution on the bottom surface (Fig. 16). Overall, the current exhibited a uniform distribution across the bottom surface. In addition, its intensity was substantially lower than that induced by the x-polarized incident wave (Fig. 13). These results indicated that the structure’s scattering behavior was dominated by the uniform magnetic current of the y-polarized incident wave.
Fig. 16. Current distribution on the bottom surface for a y-polarized incident wave (each orange rectangle represents a copper line).
3.4 Dispersion diagram
The dispersion diagram illustrates the relationship between the frequency and the propagation constant (i.e., in-plane wavevector) of a unit cell. It can be used to determine whether a specific eigenmode exists at the frequency under consideration. We employed the HFSS eigenmode solver to generate the dispersion diagram of the unit cell. A master-slave periodic boundary condition was applied in the simulation; the top and bottom surfaces of the air box were taken to be the perfectly matched layer (PML) boundary.
The dispersion curve in Fig. 17 resembles the curve of a surface plasmon polariton (SPP) that exists at the interface between a metal and a dielectric material [51–54]. The asymptotic (i.e., effective plasma) frequency was 5.82 GHz which is fairly close to the calculated resonant frequency (5.76 GHz) based on the transverse resonance condition. We concluded that the resonant frequency generated from the HFSS eigenmode solver is equal to the resonant frequency calculated based on the transverse resonance condition. At that frequency, the incident wave cannot pass through the structure, and its intensity exponentially decays in the direction of propagation (z).
Fig. 17. Dispersion diagram of a unit cell, where p is the period of the unit cell and β is the propagation constant in the transverse direction.
4. Parametric study
4.1 Circumference of the ring slot
From our full-wave simulation results, we speculated that the absorption frequency was dominated by the circumference S of the ring slot. To confirm our conjecture, we simulated our PMA with various S values. Parameter S was defined in Section 3.3, and it can be calculated using the method outlined in Fig. 12. According to the simulation results (shown in Fig. 18), the absorption frequency is inversely proportional to the circumference S. These results confirm our speculation, that is, that the absorption mechanism can be explained by transverse resonance. In Fig. 18, the absorption rate decreases when the circumference S deviates from 31.7 mm. Generally, the y component of a k vector (ky) is 2π/L (where L denotes the period) for a surface wave, and the value of L increases if the size of the ring slot increases, with no change in the separation between elements. This means that different values of S correspond to various ky values and the absorption rate is sensitive to the circumference.
4.2 Substrate thickness
To determine the role of substrate thickness d in the absorption mechanism, we simulated our proposed PMA with different thicknesses and observed the absorption rate. According to the simulation results (shown in Fig. 19), the absorption frequency does not considerably change with the thickness. However, the absorption rate clearly varied with d such that the absorption rate was lower for suboptimal values of d. Specifically, when d decreased to 0.4 mm, another absorption peak was detected in a higher frequency band. This was due to the near-field interaction between the different layers.
Our simulations suggest that the absorption frequency of our proposed PMA is related to the resonant frequency of the ring slot. However, because the substrate thickness d does not drastically affect the resonance of the ring slot, it does not affect the absorption frequency. However, the radiative damping rate affects the absorption rate [45,46] and varies with thickness d. Therefore, to maximize the absorption rate, the thickness must be optimized.
5. Experimental results
We employed the free-space method (i.e., over-the-air testing) to measure the reflection and transmission coefficients of our prototype in an anechoic chamber. We constructed a 224 × 224 mm2 prototype with 14 × 14 unit cells. The ring-slot arrays were printed on both sides of the FR4 substrate. The FR4 substrate had a thickness of 0.8 mm and a relative permittivity of 4.4. Figure 20 shows a schematic of over-the-air testing. The sample and measurement setup is illustrated in Fig. 21. To measure the reflection and transmission coefficients, we positioned a standard horn and the device under test (DUT) at a distance of 1 m from each other. To measure transmittance, two standard horns were positioned at a distance of 2 m from each other. The horn antenna was then connected to an Agilent E5071c ENA network analyzer. To measure the transmission coefficient, we recorded the transmitted signal propagating through the DUT and free space. The transmitted signal from a direct free-space path was used to normalize the signal from the DUT; the standard horns were positioned on each side of the DUT. Furthermore, we used the reflection of the metal plane (224 × 224 mm2) to calibrate the reflection coefficient. We positioned the two standard horns side by side, with their middle point aligned with the center of the DUT. The two horns were positioned close together to obtain measurements at normal incidence.
Fig. 21. Fabricated prototype and experimental setup. (a) Fabricated prototype. (b) S21 measurement. (c) S11 measurement.
The simulated and measured results are plotted in Fig. 22. The absorption frequency of the measured signal was 5.65 GHz for the x-polarized wave propagating along the −z-direction, indicating a discrepancy of 3.4% with the simulation results. Along the z-direction, the absorption frequency and discrepancy of the x-polarized measured signal were 5.63 GHz and 3.8%, respectively. Generally, environmental noise and cable lines may result in ripples and unpredicted frequency offsets in the measured signal. Fabrication imperfections, substrate nonuniformity, material impurities in the prototype, and free-space measurement tolerance [55] may also induce discrepancies. Despite slight deviations resulting from fabrication and measurement limitations, the measured and simulation results were fairly consistent with each other. Therefore, we concluded that the simulation results closely corresponded to their experimental counterparts.
Fig. 22. Simulated and measured results of the proposed PMA. (a) Absorption rate for an x-polarized wave propagating in the −z-direction. (b) Absorption rate for an x-polarized wave propagating in the + z-direction. (c) Scattering coefficients for an x-polarized wave propagating in the −z-direction. (d) Scattering coefficients for an x-polarized wave propagating in the + z-direction. (e) Scattering coefficients for a y-polarized wave propagating in the −z-direction. (f) Scattering coefficients for a y-polarized wave propagating in the + z-direction.
6. Frequency scalability of the proposed PMA
We hypothesized that because of its resonant structure, the physical dimensions of the proposed PMA would be proportional to the operating wavelength. Hence, decreasing the geometrical parameters of the proposed structure would shift its operating frequency to the terahertz band. To validate this hypothesis, we set the operating frequency to 2 THz and reengineered our PMA. We then replaced FR4 with SiO2 (permittivity = 3.5) as the dielectric substrate because FR4 performs poorly as a substrate in the terahertz band. We also used silver (conductivity = 6.3 × 107 S/m) instead of copper as the printed conductor layer. Because silver is dispersive, we set its permittivity to be (1.77 × 3.87i) × 105 at 2 THz [10].
The original PMA operated at a wavelength of λ1 = 3 × 108/(2.7)0.5 × (5.85 × 109)−1, whereas the redesigned structure operated at a wavelength of λ2 = 3 × 108/(2.25)0.5 × (2 × 1012)−1, where 2.25 is the average of the relative permittivity values of vacuum and SiO2. Using the scaling coefficient sc = λ2/λ1, we scaled down all the geometric parameters of the structure by a factor of sc. We also slightly fine-tuned the structure to increase its absorption rate from 94.9% to 97.5%. Consequently, we realized a PMA that can operate at 2 THz (with an absorption rate of 97.5% and an insertion loss of 0.255 dB). Figure 23 depicts the geometry of the unit cell, and its performance is summarized in Fig. 24. The design parameters shown in Fig. 23 are detailed in Table 3. In summary, we shifted the operating frequency of the proposed design by scaling down its physical dimensions, with the main limitation originating from the nanofabrication technology.
Fig. 24. Frequency response of the redesigned absorber for usage in the terahertz band. Absorption rate of an x-polarized wave propagating in the (a) −z-direction and (b) +z-direction. Scattering coefficients of a y-polarized wave propagating in the (c) −z-direction and (d) +z-direction.
Table 3. Detailed unit cell parameters
7. Conclusion
Herein, we propose a novel compact bidirectional PMA with two functionalities at the same wavelength. This PMA functions as a bidirectional absorber of x-polarized waves and a transparent surface for y-polarized waves. The structure also exhibits angular stability and performs well even at an incident angle of 45°. This bidirectional PMA has a cascaded ring slot array. The distance from the slot array printed on one side to the one printed on the other side is 6.2 mm in the y-direction. We validated our design by examining the E-field distribution on the surface of our structure. We confirmed that a standing wave in the transverse direction is induced only by an x-polarized incident wave. For y-polarized incident waves, the conductor pattern performs similarly to a planar uniform magnetic current source. We also verified our proposed design through experimental measurement. The experimental results had a fair agreement with the simulation results. In conclusion, the connections between neighboring ring slot elements can be used to realize a bidirectional PMA with different functionalities. The realized structure would be useful in different applications, such as in full-duplex communication systems, WPCNs, and TM polarization filters.
Appendix
According to the Ref. [50], the transverse resonance condition (TRC) of the plane considered can be expressed as follows:
where $Z_{in}^u$(r) and $Z_{in}^d$(r) are the input impedance values in the + z-direction (one side) and −z-direction (the other side), respectively, and r is the coordinate of the observation point on the plane. Alternatively, the TRC can be described using input admittance as follows: where $Y_{in}^u$(r) and $Y_{in}^d$(r) are the input admittance values in the + z- and −z-directions, respectively. Our goal here is to verify that the bottom surface of the absorber satisfies the TRC at the absorption frequency. To extract the input admittance values of the bottom surface, we simulated the structures shown in Figs. 25(b) and 25(c).Fig. 25. Schematic of the simulation setup. (a) Entire structure, (b) upper side, and (c) lower side.
We performed a full-wave simulation to retrieve the scattering coefficients ${S_{ij}}$ and $S_{ij}^u$, as shown in Fig. 25. In addition, we considered the composite structure rather than the ring slot alone because the resonant frequency of the ring slot may be affected by the surrounding medium. Subsequently, we derived the input admittance $Y_{in}^u$(r) by
where Y0 denotes the wave admittance in a vacuum. The scattering parameter $S_{11}^u$ is presented in Fig. 25. To determine the value of $S_{ij}^d$, the effect of the dielectric slab should be excluded from ${S_{ij}}$. Therefore, to solve this problem, we derived the following equation according to the Ref. [56]:Next, we calculated the scattering coefficient $S_{ij}^d$ from ${S_{ij}}$ and Eq. (10) and used Eq. (9) to calculate $Y_{in}^d$. The value of |$Y_{in}^u(r )+ Y_{in}^d(r )$| is plotted in Fig. 26.
Fig. 26. Frequency response of |${\boldsymbol Y}_{{\boldsymbol in}}^{\boldsymbol u}({\boldsymbol r} )+ {\boldsymbol Y}_{{\boldsymbol in}}^{\boldsymbol d}({\boldsymbol r} )$|.
As shown in Fig. 26, the minimum value (i.e., 0.0071, which is close to zero) was achieved at 5.96 GHz. This frequency is close to the absorption frequency (5.85 GHz), confirming that the bottom surface satisfies the TRC at the absorption frequency.
Acknowledgments
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.
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