Ultrathin Narrowband and Bidirectional Perfect Metasurface Absorber

: The conventional design approaches for achieving perfect absorption of electromagnetic (EM) waves using metasurface absorbers (MSAs) are limited to absorbing waves in one direction while reﬂecting waves in the other. In this study, a novel ultrathin narrowband MSA with bidirectional perfect absorption properties has been proposed, based on a tri-layer metal square-circular-square patch (SCSP) structure. The simulation results demonstrate that the proposed MSA exhibits a remarkable absorbance of 98.1%, which is consistent with the experimental and theoretical calculations. The equivalent constitutive parameters that were retrieved, as well as the simulated surface current and the power loss density distributions, reveal that the perfect absorption of the designed MSA originates from the fundamental dipolar resonance. Furthermore, the proposed MSA demonstrates stable wide-angle absorption properties for both transverse electric (TE) and transverse magnetic (TM) waves under various oblique incidence angles. The absorption characteristics of the MSA can be ﬁne-tuned by adjusting the structural parameters. Additionally, the proposed MSA boasts excellent ultrathin thickness, bidirectional, polarization-insensitive, and wide-angle properties, making it highly suitable for a range of potential applications such as imaging, detection, and sensing.

Numerous MSAs have been proposed and extensively studied to achieve various applications [33][34][35][36][37][38][39][40][41][42][43]. Typically, these MSAs comprise tri/multi-layer structures consisting of a metal pattern layer, a dielectric isolation layer, and a ground plane layer. The fundamental physics behind their perfect absorption is attributed to the resonant coupling between the metallic resonator structure and the ground plane, which induces wave impedance matching and EM losses [16,17]. The perfect absorption of these MSAs can be customized by altering the size, shape, and EM properties of the unit cell structure. However, most of the current designs only allow absorption of EM waves in one direction while reflecting waves in the other due to the use of a complete metal film as the ground plane. The potential application prospects of MSAs can be further expanded by implementing bidirectional perfect absorption [44][45][46][47][48][49][50][51][52]. Direction-insensitive absorption is a less explored and more challenging area in MSAs. A new approach called coherent perfect absorption has been employed to achieve bidirectional perfect absorption at optical frequencies [44][45][46]. For instance, Huang et al. proposed a multi-band MSA based on four-sized metal patches that achieved coherent perfect absorption in the infrared region [46]. Subsequently, Huynh et al. presented a tunable MSA by combining symmetric MMs and patterned graphene, achieving electrically switchable bidirectional absorption at THz frequencies [49]. Although these MSAs can realize bidirectional perfect absorption, their absorption efficiency heavily depends on the phase difference between the two coherent waves, limiting their applications to a great extent.
In contrast to previous approaches, we have proposed a novel and ultrathin narrowband bidirectional MSA, based on a tri-layered metal square-circular-square patch (SCSP) structure, with two dielectric substrate spacers. Our proposed MSA showcases bidirectional properties, enabling the absorption of EM waves with absorbance exceeding 95% from both sides of the sample plane, due to the inherent symmetry of the designed unit cell structure. Our study includes a detailed presentation of the design, measurements, and theoretical analysis of the bidirectional MSA. We then explore the underlying physics mechanisms behind the observed perfect absorption, with a focus on the effective EM parameters, surface current distributions, power flow, and power loss density distributions. Additionally, we study the absorption performance for oblique incidence of both transverse electric (TE) and transverse magnetic (TM) modes and systematically analyze the impacts of the geometrical parameters on the absorption of the MSA. Figure 1 depicts the optimized design of the proposed bidirectional MSA, consisting of a bilayer of square patches (SPs) and a middle layer of a circular patch (CP), all spaced by a dielectric substrate. As illustrated in Figure 1a, the MSA is capable of completely absorbing incident plane EM waves propagating along both the forward (+z) and backward (−z) directions at the desired operating frequency, while partially transmitting other frequencies.

Structure Design, Simulation, and Experiment
The unit cell structure of the designed MSA is shown in Figure 1b-d from a perspective, lattice, and front view, respectively. The SPs and CP patterns are made of copper, 0.01 mm thick, and have a conductivity of 5.8 × 10 7 S/m. The dielectric substrate layer is made of glass epoxy FR-4(loss), 0.2 mm thick, with a dielectric constant of 4.3 and a loss tangent of 0.025.
The absorption performance of the proposed MSA was studied through full-wave numerical simulations using the finite difference time domain (FDTD) method. This simulation allowed for the optimization of the unit cell structure's geometrical parameters and the analysis of its absorption mechanism. Since the MSA is made up of a periodic unit cell structure, the simulation focused on the performance of the unit cell rather than the overall performance of the entire MSA slab. The simulation utilized periodic boundary conditions along the x and y axes, and the wave vector (k) was perpendicular to the SCSP structure with propagation along both forward (+z) and backward (−z) directions (as shown in Figure 1a). The absorption performance of the proposed MSA was evaluated by using an X band plane wave with linear polarization, incident on the unit cell structure along the +z and −z axis directions, respectively. The absorbance was calculated using the equation 21 (ω)| 2 , where S 11 (ω) and S 21 (ω) are the reflection and transmission coefficients, respectively, as a function of frequency. In the X band, the optimization of the geometrical geometric parameters for the unit cell structure of the MSA involves finding the optimal values for parameters. The optimization process may involve iterative adjustments to find the optimal values for geometric parameters (p, r, t, and l) that lead to the desired absorption characteristics in the X band. This optimization approach helps in tailoring the MSA to specific applications and requirements within the X band frequency range. The geometrical parameters of the MSA unit cell structure were finally optimized to be p = 10 mm, r = 5 mm, t s = 0.2 mm, t p = 0.01 mm, t = 2 * t s , and l = 7 mm. The absorption level of the MSA can be adjusted by changing the sizes of the front and back metal SPs and dielectric substrate layer. The absorption performance of the proposed MSA was studied through full-wave numerical simulations using the finite difference time domain (FDTD) method. This simulation allowed for the optimization of the unit cell structure's geometrical parameters and the analysis of its absorption mechanism. Since the MSA is made up of a periodic unit cell structure, the simulation focused on the performance of the unit cell rather than the overall performance of the entire MSA slab. The simulation utilized periodic boundary conditions along the x and y axes, and the wave vector (k) was perpendicular to the SCSP structure with propagation along both forward (+z) and backward (−z) directions (as shown in Figure 1a). The absorption performance of the proposed MSA was evaluated by using an X band plane wave with linear polarization, incident on the unit cell structure along the +z and −z axis directions, respectively. The absorbance was calculated using the equation where S11(ω) and S21(ω) are the reflection and transmission coefficients, respectively, as a function of frequency. In the X band, the optimization of the geometrical geometric parameters for the unit cell structure of the MSA involves finding the optimal values for parameters. The optimization process may involve iterative adjustments to find the optimal values for geometric parameters (p, r, t, and l) that lead to the desired absorption characteristics in the X band. This optimization approach helps in tailoring the MSA to specific applications and requirements within the X band frequency range. The geometrical parameters of the MSA unit cell structure were finally optimized to be p = 10 mm, r = 5 mm, ts= 0.2 mm, tp= 0.01 mm, t = 2*ts, and l = 7 mm. The absorption level of the MSA can be adjusted by changing the sizes of the front and back metal SPs and dielectric substrate layer. To further verify the efficacy of the proposed bidirectional MSA, a microwave experiment was conducted. The test sample of the MSA was fabricated through the conventional printed circuit board (PCB) technology, employing the optimized geometric parameters of the unit cell structure. The fabricated MSA test sample, with dimensions of 180 mm × 180 mm × 0.43 mm, consisted of 18 × 18 unit cells, as depicted in Figure 2a. Subsequently, the microwave measurement was performed in an EM anechoic chamber, using a network analyzer (Agilent N5244A PNA-X, Agilent, Santa Clara, CA, USA) connected to two standard horn antennas, to record the reflection and transmission coefficients of the MSA sample. The distance between the horn antennas and the MSA sample was set to 2 m in the microwave measurement, considerably greater than the operational wavelength, to eliminate the near-field effect [53].
Coatings 2023, 13, 1340 4 of 12 mm × 180 mm × 0.43 mm, consisted of 18 × 18 unit cells, as depicted in Figure 2a. Subse-quently, the microwave measurement was performed in an EM anechoic chamber, using a network analyzer (Agilent N5244A PNA-X, Agilent, Santa Clara, CA, USA) connected to two standard horn antennas, to record the reflection and transmission coefficients of the MSA sample. The distance between the horn antennas and the MSA sample was set to 2 m in the microwave measurement, considerably greater than the operational wavelength, to eliminate the near-field effect [53].

Results and Discussions
Figure 2b,c depicts the simulated and measured reflectance, transmittance, and absorbance spectra of the proposed MSA when a normal incident plane wave propagates along the forward (+z) axis direction (see Figure 1a). The measured results are in good agreement with the simulations, with minor discrepancies attributed to the inaccurate model of the copper film, limited sample size, and fabrication and measurement tolerances. As shown in Figure 2b, the simulated transmittance is less than 0.1 across the entire X band of 8-12 GHz, with an almost zero value at the resonance frequency of 10 GHz. Notably, a prominent reflection dip occurs at 10 GHz, with a reflectance of only about 1.23% and an absorbance of up to 98.1%. To assess the narrowband absorption properties, we calculated the full width at half maximum (FWHM) and the Q factor from the simulated absorbance, resulting in values of 0.5 GHz and approximately 20, respectively. As shown in Figure 2c, the measured absorbance is nearly perfect at 96.16%. In addition, the total thickness of the proposed MSA is only 0.43 mm, which is about λ/69.76 at 10 GHz, where λ is the corresponding absorption wavelength, revealing an ultrathin property.
In order to verify the bidirectional absorption performance of the proposed MSA, a comparison of the simulated and measured absorbance spectra was conducted. The MSA was illuminated by a normal incident planar EM wave propagating along both the forward (+z) and backward (−z) axis direction, as depicted in Figure 3b. The observed similarity between the simulated and measured absorption curves for both forward and backward incidence confirms the presence of typical bidirectional absorption. This phenomenon can be explained through the critical coupled mode theory (CMT), which provides a framework for the suppression of both reflection and transmission, leading to an enhancement in light absorption [54][55][56]. The CMT has been extensively utilized to interpret the perfect absorption properties of the MSA [24,26,32]. The proposed MSA structure can be considered as a coupling system, where critical coupling is employed to achieve perfect absorption by coupling the localized resonance mode to the lossy SCSP structure. This design allows for localized resonance mode, resulting in a significant confinement of the EM field within the SCSP structure of the MSA. Consequently, the incident EM wave can couple with the mode resonance, leading to a highly enhanced absorption in the vicinity of the resonance frequency. The proposed tri-layered structure of the MSA enables phase-matched coupling between the EM resonance and free-space radiation, confining the EM field significantly within the MSA structure. The CMT was used to calculate the absorbance of the MSA structure, which is expressed as [32]: where ω is frequency of the incident EM wave, ω 0 represents the resonance frequency, and γ e and δ e represent the external leakage time rate of the amplitude change and the dissipative intrinsic losses in the EM resonance of the MSA slab, respectively. The absorbance spectrum for normal forward (+z) incidence was compared using simulation, experiment, and CMT fitting and is depicted in Figure 3b. The comparison shows that the simulation of the proposed MSA, CMT, and experiment results are highly consistent across the entire X band frequency range. The absorption mechanism of the proposed bidirectional MSA can also be further elucidated by analyzing the equivalent EM parameters using the effective medium theory [30,57,58]. A substantial imaginary component of the equivalent EM parameters can ensure EM energy dissipation and strong absorption. Designing the unit cell structure of the bidirectional MSA to adjust the equivalent EM parameters enables efficient absorption. The EM parameters of the bidirectional MSA can be obtained by retrieving the simulated S-parameters (S 11 and S 21 ) [57,58].
The retrieved constitutive EM parameters (equivalent relative refraction index n, permittivity ε, and permeability µ and wave impedance z) are depicted in Figure 4a-d. It can be seen that the real part of the equivalent permittivity, permeability, and refractive index (Re(ε), Re(µ), and Re(n)) are negative around the absorption peak frequency, as shown in Figure 4a-c. The proposed MSA structure exhibits a strong electrical and magnetic resonance response to normal incident EM waves and demonstrates negative refraction. The negative permittivity is attributed to a strong plasmonic and electrical dipolar resonance response to the electric field of the incident EM wave, while the negative permeability is a result of a magnetic dipolar resonance response to an external magnetic field. Additionally, the highest microwave attenuation occurs around the resonance frequency of 10 GHz, as indicated by the maximal value of the imaginary part of the relative refractive index (Im(n)). The high absorption level of the bidirectional MSA is primarily due to the fundamental electrical and magnetic resonance loss, which is significantly different from the coherent absorption mechanism employed by previous optical absorbers [44][45][46][47][48][49]. The real part of Coatings 2023, 13, 1340 6 of 12 the equivalent relative wave impedance (Re(z)) is approximately unity, while the imaginary part (Im(z)) is near zero at the absorption frequency, indicating that the wave impedance of the designed bidirectional MSA can be closely matched to free space around the resonance frequency.
Coatings 2023, 13, x FOR PEER REVIEW 6 of 13 Figure 3. The (a) comparison of the simulated and measured absorbance spectra of the proposed bidirectional MSA for normal forward (+z) and backward (−z) incidence; (b) the comparison of absorbance spectra from the simulation, theory, and experiment for normal forward (+z) incidence.
The absorption mechanism of the proposed bidirectional MSA can also be further elucidated by analyzing the equivalent EM parameters using the effective medium theory [30,57,58]. A substantial imaginary component of the equivalent EM parameters can ensure EM energy dissipation and strong absorption. Designing the unit cell structure of the bidirectional MSA to adjust the equivalent EM parameters enables efficient absorption. The EM parameters of the bidirectional MSA can be obtained by retrieving the simulated S-parameters (S11 and S21) [57,58].
The retrieved constitutive EM parameters (equivalent relative refraction index n, permittivity ε, and permeability µ and wave impedance z) are depicted in Figure 4a-d. It can be seen that the real part of the equivalent permittivity, permeability, and refractive index (Re(ε), Re(µ), and Re(n)) are negative around the absorption peak frequency, as shown in Figure 4a-c. The proposed MSA structure exhibits a strong electrical and magnetic resonance response to normal incident EM waves and demonstrates negative refraction. The negative permittivity is attributed to a strong plasmonic and electrical dipolar resonance response to the electric field of the incident EM wave, while the negative permeability is a result of a magnetic dipolar resonance response to an external magnetic field. Additionally, the highest microwave attenuation occurs around the resonance frequency of 10 GHz, as indicated by the maximal value of the imaginary part of the relative refractive index (Im(n)). The high absorption level of the bidirectional MSA is primarily due to the fundamental electrical and magnetic resonance loss, which is significantly different from the coherent absorption mechanism employed by previous optical absorbers [44][45][46][47][48][49]. The real part of the equivalent relative wave impedance (Re(z)) is approximately unity, while the imaginary part (Im(z)) is near zero at the absorption frequency, indicating that the wave impedance of the designed bidirectional MSA can be closely matched to free space around the resonance frequency.  To provide further insight into the absorption mechanism of the designed bidirectional MSA, the surface current distribution on the front and middle layers of the unit cell structure at the absorption peak frequency of 10 GHz is presented in Figure 5. The results reveal that the induced surface current on the front and middle layers of the unit cell structure is antiparallel along the y-axis direction, indicating a typical magnetic dipolar resonance. Despite the fact that the MSA is constructed solely of nonmagnetic metallic and  To provide further insight into the absorption mechanism of the designed bidirectional MSA, the surface current distribution on the front and middle layers of the unit cell structure at the absorption peak frequency of 10 GHz is presented in Figure 5. The results reveal that the induced surface current on the front and middle layers of the unit cell structure is antiparallel along the y-axis direction, indicating a typical magnetic dipolar resonance. Despite the fact that the MSA is constructed solely of nonmagnetic metallic and dielectric substrate, the circulating surface currents driven by the capacitance between the SP front layer and the CP middle layer constitute the sole source of magnetic resonance, which is consistent with the retrieved equivalent permeability. This observation further confirms that the combination of fundamental electrical and magnetic resonance loss leads to the stronger absorption of the proposed MSA. In order to better understand the absorption mechanism of the designed bidirectional MSA, it is important to visually identify where and how the strong absorption occurs. Figure 6 presents the power flow and loss density on the front and back space surfaces of the MSA unit cell structure for the normal incident EM wave propagating along the forward (+z) and backward (−z) direction at resonance. As depicted in Figure 6a,b, it can be observed that the incoming wave power flows propagating along the forward (+z) and backward (−z) direction are both parallel at a far distance from the unit cell structure. However, when the incoming power flows reach the vicinity of the front and back surface of the unit cell structure, they curl inside the SP structure and eventually distribute in the internal area of the dielectric substrate. This process allows for easy gathering and focusing of the power flows on the interior of the unit cell structure, ultimately resulting in complete absorption. Additionally, as shown in Figure 6c,d, the power loss densities are mainly concentrated on the upper and lower areas of the front and back SP structure, respectively, for the incident wave propagating along the forward (+z) and backward (−z) direction. This demonstrates that the incident EM wave energy is effectively confined in the square patch area of the designed bidirectional MSA, with no waves being reflected at resonance.
It is imperative to evaluate the impact of varying polarization and incident angles on the absorption performance of the proposed bidirectional MSA. Due to the high degree of geometrical rotational symmetry in the unit cell structure, the MSA should ideally demonstrate polarization insensitivity when propagating normal incident waves along both the forward (+z) and backward (−z) directions for both TE and TM modes (not shown). In this analysis, we focus on the oblique incident angle dependencies of the MSA on both TE and TM modes. In order to better understand the absorption mechanism of the designed bidirectional MSA, it is important to visually identify where and how the strong absorption occurs. Figure 6 presents the power flow and loss density on the front and back space surfaces of the MSA unit cell structure for the normal incident EM wave propagating along the forward (+z) and backward (−z) direction at resonance. As depicted in Figure 6a,b, it can be observed that the incoming wave power flows propagating along the forward (+z) and backward (−z) direction are both parallel at a far distance from the unit cell structure. However, when the incoming power flows reach the vicinity of the front and back surface of the unit cell structure, they curl inside the SP structure and eventually distribute in the internal area of the dielectric substrate. This process allows for easy gathering and focusing of the power flows on the interior of the unit cell structure, ultimately resulting in complete absorption. Additionally, as shown in Figure 6c,d, the power loss densities are mainly concentrated on the upper and lower areas of the front and back SP structure, respectively, for the incident wave propagating along the forward (+z) and backward (−z) direction. This demonstrates that the incident EM wave energy is effectively confined in the square patch area of the designed bidirectional MSA, with no waves being reflected at resonance.
It is imperative to evaluate the impact of varying polarization and incident angles on the absorption performance of the proposed bidirectional MSA. Due to the high degree of geometrical rotational symmetry in the unit cell structure, the MSA should ideally demonstrate polarization insensitivity when propagating normal incident waves along both the forward (+z) and backward (−z) directions for both TE and TM modes (not shown). In this analysis, we focus on the oblique incident angle dependencies of the MSA on both TE and TM modes.  Figure 7a,b presents the simulated absorbance of the MSA with varying incident angles ranging from 0° to 75° for TE and TM modes, respectively. As depicted in Figure 7a, the proposed MSA exhibits exceptional absorption performance for the TE mode when the incident angle is below 50°. However, beyond 50°, the absorbance gradually decreases due to the reduction in the magnetic field component, making it difficult to excite the magnetic resonance at higher incident angles. Conversely, for the TM mode, the absorption performance of the MSA remains almost unaffected by different oblique incident angles, as shown in Figure 7b. Nevertheless, the resonance absorption frequency slightly blue shifts when the incident angle of TM mode exceeds 60° due to higher-order resonance or parasitic capacitance response. Thus, the proposed MSA retains an exceptional narrowband absorption performance over a wide angle for both TE and TM mode oblique incidence.  Figure 7a,b presents the simulated absorbance of the MSA with varying incident angles ranging from 0 • to 75 • for TE and TM modes, respectively. As depicted in Figure 7a, the proposed MSA exhibits exceptional absorption performance for the TE mode when the incident angle is below 50 • . However, beyond 50 • , the absorbance gradually decreases due to the reduction in the magnetic field component, making it difficult to excite the magnetic resonance at higher incident angles. Conversely, for the TM mode, the absorption performance of the MSA remains almost unaffected by different oblique incident angles, as shown in Figure 7b. Nevertheless, the resonance absorption frequency slightly blue shifts when the incident angle of TM mode exceeds 60 • due to higher-order resonance or parasitic capacitance response. Thus, the proposed MSA retains an exceptional narrow-band absorption performance over a wide angle for both TE and TM mode oblique incidence. Further, we undertake a comprehensive and systematic investigation of the impact of geometric parameters on the absorption properties of the bidirectional MSA. Our analysis focuses on two key parameters: the dielectric layer thickness (t) and side length (l) of the square patch. Figure 8a depicts the absorbance spectra with t varying from 0.2 mm to 1.0 mm. The operation frequency remains nearly unchanged with changes in t. However, the absorbance initially increases and then gradually decreases as t increases, reaching its maximum value at t = 0.4 mm. This is due to the coupling magnetic resonance, which initially weakens, then strengthens, and weakens again with increasing MSA thickness. At t = 0.4 mm, the coupling magnetic resonance reaches its maximum, resulting in nearperfect absorption.  Further, we undertake a comprehensive and systematic investigation of the impact of geometric parameters on the absorption properties of the bidirectional MSA. Our analysis focuses on two key parameters: the dielectric layer thickness (t) and side length (l) of the square patch. Figure 8a depicts the absorbance spectra with t varying from 0.2 mm to 1.0 mm. The operation frequency remains nearly unchanged with changes in t. However, the absorbance initially increases and then gradually decreases as t increases, reaching its maximum value at t = 0.4 mm. This is due to the coupling magnetic resonance, which initially weakens, then strengthens, and weakens again with increasing MSA thickness. At t = 0.4 mm, the coupling magnetic resonance reaches its maximum, resulting in near-perfect absorption. Further, we undertake a comprehensive and systematic investigation of the impact of geometric parameters on the absorption properties of the bidirectional MSA. Our analysis focuses on two key parameters: the dielectric layer thickness (t) and side length (l) of the square patch. Figure 8a depicts the absorbance spectra with t varying from 0.2 mm to 1.0 mm. The operation frequency remains nearly unchanged with changes in t. However, the absorbance initially increases and then gradually decreases as t increases, reaching its maximum value at t = 0.4 mm. This is due to the coupling magnetic resonance, which initially weakens, then strengthens, and weakens again with increasing MSA thickness. At t = 0.4 mm, the coupling magnetic resonance reaches its maximum, resulting in nearperfect absorption.  As shown in Figure 8b, the changing l of the square metallic patch structure from 5 mm to 9 mm causes a gradual red shift in the operation frequency since the equivalent capacitance (C) and inductance (L) both increase according to the LC resonance circuit theory [27,59]. It can also be observed that the absorption level initially increases and then gradually decreases with increasing l, reaching its maximum value at l = 7 mm. This is because the electrical resonance initially weakens, then strengthens, and weakens again with the increasing side length of the square patch of the MSA. At l = 7 mm, the proposed MSA structure exhibits the strongest electrical resonance response, resulting in near-perfect absorption.
Based on the results of the simulation analysis, we can draw the conclusion that the absorption performance of the proposed bidirectional MSA can be adjustable by altering the geometrical parameters of the unit cell structure. By precisely optimizing these parameters, the absorption level can be maximized.

Conclusions
In summary, we have proposed and demonstrated an ultrathin and narrowband bidirectional MSA that utilizes a tri-layer metal SCSP structure spaced by a dielectric substrate in the microwave region. Unlike previous MSA structures, our proposed design achieves a stronger absorbance of over 95% from both forward (+z) and backward (−z) incidences. The equivalent EM parameters of the MSA suggest that the narrowband stronger absorption is primarily due to the electric and magnetic dipolar resonance response, which is consistent with the analysis of the surface current distributions. Furthermore, our proposed MSA exhibits wide angular absorption performance for incident angles up to approximately 50 • for both TE modes and 60 • for the TM mode. Our additional simulations indicate that the resonance absorption performance of the MSA can be adjusted by modifying the geometric parameters of the unit cell structure, allowing for the identification of optimal parameters for achieving maximum absorption levels. Additionally, due to the MS inherent properties, our bidirectional perfect absorption properties can be applied in millimeter wave, terahertz, or even optical ranges by reducing the dimensions of the proposed MSA structure to micro-, nano-, and lower scales. This ultrathin and narrowband bidirectional MSA has the potential for numerous applications in communication, sensing, detection, and other areas.