A compact frequency-selective absorber with optical transparency

This article proposes a new method for designing an optical transparent frequency-selective surface absorber using indium tin oxide (ITO) conductive film with different sheet resistances. This novel optical transparent frequency-selective absorber exhibits excellent optical transparency, ensuring a visible light transmittance exceeding 76%. Simultaneously, it exhibits broadband absorption characteristics covering the entire X-Ku band, with an absorption rate exceeding 90%. Due to the simplicity of the design, the overall structure is easily processable, and the desired product can be rapidly fabricated using laser etching equipment without adding any lumped elements in the design. Simulation and experimental results indicate that the S11–10 dB frequency range of the frequency-selective absorber is 7.7–18.4 GHz, with a transmission frequency range below −3 dB between 26.7–29.4 GHz. The findings suggest that this structure holds potential applications in microwave stealth design requiring optical transparency and high-throughput satellite communication scenarios.


Introduction
The artificial electromagnetic metasurface has gained widespread attention and applications due to its low cost and efficient control of electromagnetic wavefronts.The functionalities of electromagnetic metasurfaces include wavefront control with reflection and transmission capabilities, frequency-selective surfaces that modulate amplitude, and electromagnetic perfect absorbers that completely absorb incident waves [1][2][3][4].A frequencyselective surface (FSS) is a two-dimensional periodically arranged array structure that exhibits different responses to electromagnetic waves of varying frequencies, polarizations, and incident angles.Over the past two decades, FSS has found widespread applications in hybrid radar antenna radomes, wave polarizers, and electromagnetic interference prevention [5].To further enhance the stealth performance of FSS design, an integrated design with metamaterial absorbers, known as superstrate absorbers, has been proposed.From the relationship between absorption bands and transmission windows, FSS absorbers can be classified into three types: (1) low-frequency absorption and high-frequency transmission [6,7] (2) low-frequency transmission and high-frequency absorption [8,9], and (3) absorption bands on both sides of the passband [10][11][12].Metamaterial absorbers are a type of artificial, sub-wavelength, two-dimensional structure capable of absorbing specific frequency bands of electromagnetic waves [13,14].Recently, a special class of optical transparent metamaterial absorbers has gained widespread attention.These absorbers, which absorb specific frequency bands of electromagnetic waves, also achieve visible light transparency.This holds extraordinary significance for microwave applications in optically transparent scenarios.Researchers, including Cui Tiejun from Southeast University, have proposed a class of optically transparent metamaterial absorbers characterized by their ultrathin thickness, broadband absorption, and mechanical flexibility [15].However, due to design limitations, the number of designs for optically transparent frequency-selective absorbers remains limited.
The key to designing an optically transparent frequency-selective absorber lies in the top-layer lossy absorption layer and the bottom frequency-selective passband layer.To ensure optical transparency of the overall structure, transparent substrate materials, transparent metallic materials, or conductive thin films are chosen for the design.However, the electrical conductivity of most transparent metallic materials is relatively low, causing parallel resonance in the passband frequency and higher insertion losses [16,17].To achieve broadband absorption, the surface loss layer needs to achieve low-Q-value series resonance within the absorption frequency band.Since the overall structure requires optical transparency, no lumped elements can be used in the surface loss layer, imposing higher requirements for simplicity and thinness in the design [18][19][20][21].
This paper proposes a transparent frequency-selective absorber with wideband microwave absorption capability, high optical transparency, and a transmission window with low insertion loss at high frequencies.It consists of two functional layers and an air layer, independently controlling microwave absorption and transmission.Its structure and functional schematic diagram are shown in figure 1 below.The proposed structure includes a topological cross-shaped resonator based on ITO coating as the absorption layer and a square ring aperture frequency-selective surface as the transmission layer, with both layers separated by a quartz glass dielectric layer.Equivalent circuit models, full-wave numerical simulations, and measurement results are provided, demonstrating good agreement between measured and simulated results.Additionally, for the first time, the passband frequency has been extended to the Ka band, and numerical simulation results indicate that the center frequency is around 28 GHz, with a −3 dB bandwidth covering 25-30 GHz, meeting the requirements of 5 G millimeter-wave communication and integrated communication between air and ground.This paper analyzes the principles of the frequency-selective absorber (FSA) through equivalent circuit models and field distribution exploration, and experimental verification is conducted on processed samples.
The experimental results fit well with the simulation results, proving the performance of the sample.This design can be applied in any scenario requiring both optical transparency and radar stealth effects, including hybrid radar antenna radomes, aircraft cockpit glass, vehicle optical transparent windows, and architectural optical observation windows.

Structure design
The top-layer lossy absorption layer serves two primary purposes.Firstly, it utilizes the frequency-selective passband layer at the bottom of the structure to act as a grounding metal layer, collectively absorbing electromagnetic waves outside the passband frequency.Second, at the passband frequency, it provides a low insertion loss transmission window.The evolution of the top-layer lossy absorption layer and its corresponding equivalent circuit model is illustrated in figure 2.
As shown in figure 2, the unit selected for the top-layer lossy absorption layer in our design uses the Jerusalem cross unit as the basic structural element.This unit consists of a pair of crossed dipoles with terminal loading capacitors.Due to the presence of terminal capacitors, the Jerusalem cross unit extends the frequency range of first-order and second-order harmonic modes, providing a wide bandwidth and stable performance.Modeled theoretically using equivalent circuit models, the traditional Jerusalem cross can be represented by a series resonance circuit composed of inductance (L) and capacitance (C).As the top-layer lossy absorption layer employs a lossy transparent metallic material, a resistor (R) needs to be connected in series with the LC resonator.To achieve a resonant path with a longer length in the limited two-dimensional space and simultaneously reduce processing complexity, the capacitive arms loaded at both ends of the capacitor are treated separately.One end of the capacitive arm forms a central connected cross structure, and the other end extends into a topological arm with higher inductance than the previous structure.Field analysis from the diagram indicates that the two arms form a surface current lossy path, achieving specific frequency band absorption performance.
The frequency-selective passband layer transmits signals within the passband frequency and acts as a metal ground plane at non-operational frequencies.In this design, considering the total thickness of the frequencyselective absorber and design simplicity, a highly selective first-order passband structure is employed as the frequency-selective passband layer.The traditional square ring aperture unit can be equivalently represented as a parallel LC resonant circuit.The advantage of this structure lies in its thin thickness, low insertion loss, and simplicity.
Through a rational design of the top-layer lossy layer and the bottom-layer frequency-selective passband layer, the proposed structure can achieve absorption or transmission characteristics in their respective operating frequency bands.As shown in figure 3, the dielectric substrates of both the top-layer lossy layer and the bottomlayer frequency-selective passband layer are transparent.The sheet resistance of the top-layer ITO is 10 Ω, and the sheet resistance of the bottom-layer ITO is 1 Ω.Between the upper and lower quartz glass layers, there is a 1mm-thick air layer.The structure of the top-layer lossy layer consists of four fork-shaped electrodes combined with a central cross.The outer side of the fork-shaped electrodes forms a topological dipole structure.The bottom-layer frequency-selective passband layer has a square ring aperture structure, allowing low-loss transmission of electromagnetic waves at specific frequencies.The main parameters of the unit are shown in  = --Due to the adoption of a centrally symmetric pattern in the design, the structure exhibits polarization insensitivity.
This paper chooses to illustrate the impact of the top-layer sheet resistance on microwave reflectance and transmittance in the structural design.Different sheet resistance values, such as 5 Ω, 10 Ω, and 15 Ω, were selected as examples in the simulation.According to formula (1), it can be observed that the absorption bandwidth is directly proportional to the active power.
In equation (1), where f is the operating frequency, P r and P a represent reactive power and active power, respectively, it can be observed that the bandwidth is positively correlated with active power.As the sheet resistance R increases, the absorption bandwidth becomes wider.However, excessively large R can damage absorption performance due to impedance mismatch.As shown in figure 5, too small R values can affect impedance matching, reducing absorption capacity, while excessively large R values reduce bandwidth.The optimized sheet resistance value is 10 Ω, achieving a balanced performance in terms of absorption and bandwidth.

Analytical verification
In order to better study the absorption mechanism of the frequency-selective absorber, figure 6 displays the surface current distribution, electric field, and energy loss density of the overall structure under different frequencies and polarization conditions.At the absorption resonance points of 8.1 GHz and 17.7 GHz, the structure of the top-layer lossy absorption layer resonates, and the induced current mainly concentrates on the structure parallel to the incident wave's electric field direction.At the resonant frequencies of 8.1 GHz and 17.7 GHz, the overall structure's energy loss is mainly concentrated in the top layer of the structure.When the frequency is 28 GHz, the induced current is at the edges of the apertures in the bottom frequency-selective passband layer, parallel to the electric field direction of the incident wave.At the absorption resonant frequencies, the induced current mainly concentrates in the same region as the top-layer lossy absorption layer.According to Joule's law P I R,

2
= ´where P is the power consumed by the structure, I is the current density, and R is the surface resistance, the region with the highest energy loss coincides with the region of high induced current density.
According to the 2D display of the structure's electric field, it can be observed that the distribution of the electric field on the surface of the structure complements the density of the surface current distribution.The region with the strongest surface electric field is concentrated in the fork-shaped electrode part connected to the central cross arm.The side view of the electric field distribution in the structure shows that, at the absorption frequencies of 8 GHz and 18 GHz, the top absorption layer and the bottom passband layer work together.The bottom passband layer can be equivalent to a metal ground plane, reflecting the incident electromagnetic wave.The top absorption layer causes the majority of the losses.The simulated material loss plot shows that the dielectric loss caused by quartz glass is minimal, and the Ohmic loss caused by the electric resonance is the reason for the good absorption of the structure in the absorption frequency band.
From the figure 6, it can be observed that the Ohmic loss caused by the low sheet resistance of the transparent conductive film in the bottom layer at the passband frequency of 28 GHz will increase.This is due to the induced current at the edges of the bottom layer frequency-selective surface apertures in the direction of the frequency selection, leading to an increase in Ohmic loss.This, combined with the intrinsic Ohmic loss caused by contact with the top layer of the incident electromagnetic wave, contributes to the insertion loss at the passband frequency.It can be seen that the loss caused by the top absorption layer is stable in non-absorption frequency bands and slightly increases in the passband.This increase is due to the change in electric field caused by the resonance of the bottom layer frequency-selective passband layer at the passband frequency.

Durability
Frequency-selective absorbers belong to the engineering applications of surface science.Considering the performance changes of samples under different temperature and humidity conditions is necessary.The discussed performance includes the absorptance in the absorption band, insertion loss in the passband, and visible light transmittance.Due to the lack of relevant equipment in the laboratory, our discussion is mainly based on the research on the properties of ITO and quartz glass cited from other literature.First, we explore the performance changes of ITO conductive films under the influence of temperature and humidity.Studies have shown that for ITO films on glass substrates, the sheet resistance remains roughly constant below 250 °C, doubling after reaching temperatures above 250 °C and increasing to four times its original value at 600 °C [22].In another study, it was found that ITO conductive films on glass substrates with a thickness of 300 nm showed a 1.2 times increase in sheet resistance after exposure to 85 °C and 85% relative humidity for 100 h [23].After exposure for 2000 h, the sheet resistance was maintained at around 1.2 times the original value.In response to this situation, we conducted full-wave simulation on the possible scenarios.Sample A represents the original performance sample, and sample B represents a sample with a sheet resistance 1.2 times the original value.It is used to simulate extreme cases of sample resistance changes.The specific results are shown in the figure 7 below.It can be seen that the absorption amplitude of S 11 in the absorption band has increased, but the absorption bandwidth has decreased slightly.At 28 GHz, the insertion loss has slightly increased.Considering the extreme conditions of 85 °C and 85% relative humidity, the performance remains stable.The broadband absorption effect covers the X and Ku bands, and the high-frequency insertion loss is greater than the target value of −3 dB.
According to research, quartz glass shows no significant drift in the relative permittivity and loss tangent within temperatures up to 300 °C [24].Therefore, it is predicted that as long as the sheet resistance of ITO remains relatively stable, the performance of the frequency-selective absorber will not be affected by changes in the properties of quartz glass.Since quartz glass is chosen as the substrate instead of other transparent organic materials, it is unlikely that the dielectric plate will undergo yellowing due to UV-induced degradation, and there will be no potential decrease in transmittance.

Equivalent circuit model analysis
In order to better analyze the working principle of the overall structure from a general perspective, we utilized transmission line theory to model the equivalent circuit of the entire structure.The equivalent circuit model of the overall structure is shown in figure 8.In this model, the top lossy absorption layer is equivalent to a series RLC circuit [25], and the bottom frequency-selective passband layer is equivalent to a parallel RLC circuit.It is worth noting that, due to the low sheet resistance of the chosen transparent conductive material in the bottom layer, the resistance (R) of the bottom layer's frequency-selective passband layer cannot be neglected.The quartz glass dielectric layer is equivalent to a transmission line, and its electrical length is related to the relative permittivity and thickness [26,27].
For a dual-layer two-port device, where t and Z s represent the thickness and equivalent characteristic impedance of the dielectric layer, considering this model as a two-port network, the ABCD matrix can be represented as: q q q q q q q q q = = +

Experimental validation
In order to further demonstrate the effectiveness of the proposed frequency-selective absorber, a prototype sample of 120 * 120 mm was designed and manufactured for testing.The etched surface unit of the prototype sample consists of 20 * 20 elements, matching the size provided in the article.The top and bottom layers of the prototype sample are made of quartz glass with a dielectric constant of 3.779.The top layer has a thickness of 185 nm, and the bottom layer has a thickness of 1200 nm.A 1 mm air gap is reserved between the two layers.The top layer, air gap, and bottom layer structures are fixed using a PMMA fixture.The physical appearance of the assembled sample and fixture is shown in figure 9(a).The test sample exhibits good optical transparency.The installation of the test sample with the fixture is shown in the figure.
The experimental prototype sample was measured using a free-space measurement setup, which includes the transmit/receive antennas, a vector network analyzer (Ceyear N3671G), the test sample, and its fixture.Preparations before testing mainly involved aligning the antennas, fixture, and sample, as well as calibrating the vector network analyzer.To obtain clear curves, time-domain gating technology was used in the testing of the frequency-selective absorber.The comparison between the measurement results and simulation results is shown in figure 10.It can be observed that the reflection and transmission coefficients match well with the simulated data.There is a slight amplitude variation in the absorption band of S 11 , and a slight frequency drift of S 21 in the passband, mainly due to manufacturing tolerances, distance errors between the top absorbing layer and the bottom frequency-selective passband layer, and misalignment of the units during assembly.Ignoring these factors, the overall trend of the measured curves is basically consistent with the simulated curves, confirming the effectiveness of the designed frequency-selective absorber.To better showcase our advantages, we compared the performance of this structure with the performance of previous achievements.
Finally, the optical transmittance of the sample was measured using a light transmittance meter in the visible, ultraviolet, and infrared ranges, with an average transmittance of 76.9%, slightly below the target of 80%, as shown in figure 11.

Manufacturing tolerance
Manufacturing tolerances were applied, and the sheet resistance values of the bottom passband layers for samples A and B were measured using a four-probe sheet resistance meter, with values above 3 Ω.As shown in figure 12, the graph displays the sheet resistance values measured for experimental samples 1 and 2 using a fourpoint probe resistance meter.In the simulation software, we investigated potential performance issues caused by sheet resistance tolerance based on the data provided by the fabrication process.The simulation results for the sheet resistance manufacturing tolerance are shown in figure 13.Through simulation data, we explored possible performance outcomes.The results indicated that when the resistance value of the top layer with the absorbing  layer exceeded the expected 10 Ω, a downward extension of S 11 around 12 GHz was observed, reaching close to −15 dB from the −10 dB level.An increase in the resistance value of the bottom layer with the absorbing layer resulted in a certain degree of increase in insertion loss.

Interlayer misalignment
Due to issues such as the sample-fixture spacing and fixation, results in a misalignment error between the top and bottom layers within a range of 4 mm.We used CST Microwave Studio to adjust the etching pattern's position to explore potential outcomes.Figure 14 illustrates the potential performance outcomes of interlayer misalignment.In the case of slight misalignment, there may be a deeper dip in the S 11 high-frequency resonance point, while severe misalignment, approaching 4 mm, may lead to a dip in the low-frequency resonance point to   a lower level.It is observed that misalignment does not affect the variation of resonance frequency points but does have a certain impact on the amplitude.

Data error caused by the replacement of the horn antenna
Due to the wide measurement frequency range, the switching of different frequency horn antennas may have caused an abnormal amplitude drop in S 11 at 12 GHz.In the experiment, data integration was performed after switching five sets of horn antennas with different operating frequencies.The VSWR at the two ends of the standard gain horn antenna's operating frequency, namely the start and stop frequencies, was the worst, while the VSWR at the central frequency was generally better.When generating the curve, it is necessary to combine the S parameters measured with the five sets of horn antennas.At this point, issues with the initial data may arise.This can explain the abnormal resonant-like dip in S 11 at 12 GHz and the abnormal increase in S 11 at 22 GHz in the experimental data.

Performance comparison with previous frequency-selective absorbers
The results indicate that, compared with other frequency-selective absorbers, the proposed frequency-selective absorber in this study features optical transparency in the visible range, an extremely wide absorption band, the highest transmission passband frequency, and the least number of lumped elements.The frequency-selective absorber designed in this study achieves a low thickness of 0.08 a l at the lowest operating frequency.Due to the absence of any lumped elements in the unit structure, the manufacturing cost and complexity are reduced.It can be applied in various optical transparent scenarios.As shown below, table 1 presents the performance comparison between the frequency-selective absorber proposed in this study and the previous research findings.
The design is based on a mature commercial production preparation method, with the potential for largescale production and good scalability.Due to its foundation in the combination design of transparent conductive films, the dielectric substrate can be selected from other transparent materials that can be sputtered, requiring only appropriate electromagnetic parameters to achieve similar performance.Meanwhile, further design modifications can be applied to the underlying passband layer.In theory, based on practical processing or real-world requirements, higher-frequency passband effects can be achieved.

Conclusion
This article presents a low-cost solution for designing a frequency-selective absorber with low Q-value parallel resonance in the transmission band while maintaining high optical transparency.The method primarily involves the use of ITO coatings with different sheet resistances to design the absorptive layer with low loss and the low-loss passband layer, achieving high absorption in the absorption band and low insertion loss in the transmission band.Through simple etching of the film resistance coating, the absorptive layer is designed as a cross-shaped interdigitated electrode topological structure, and the bottom layer of the low-loss passband is designed as a square ring aperture structure.The overall structure exhibits high efficiency and optical transparency.According to simulation results, the structure shows S 11 <−10 dB in the frequency range of 7.7-18.5GHz with an insertion loss of approximately −1.2 dB at 28 GHz.The absorption rate exceeds 90% in the frequency range of 7.7-18.4GHz.The analysis of the structure includes both field analysis and equivalent circuit model methods.To validate the design feasibility, experimental samples were fabricated and measured, and the experimental results match well with the simulation results.

Figure 1 .
Figure 1.Schematic diagram of the proposed integrated absorption-transmission functional structure in this paper.

Figure 2 .
Figure 2. Evolution of the structure of the top-layer lossy absorption layer (a) and the equivalent circuit model evolution (b).

Figure 4 .
Figure 4. Simulation results of the S-parameters and absorption efficiency for the proposed structure in this paper.

Figure 5 .
Figure 5. Influence of Different Sheet Resistance Values on S-Parameters.

Figure 6 .
Figure 6.Surface current density, electric field plots, and surface loss density of the absorption layer and transmission layer at 8, 18, and 28 GHz.

Figure 7 . 21 2
Figure 7.Comparison of performance between standard samples and samples in high heat and humidity environments.

Figure 8 .
Figure 8.The equivalent circuit of the dual-layer frequency-selective absorber.

Figure 9 .
Figure 9. (a) Experimental sample image (b) Testing environment (c) Reflection coefficient measurement method (d) Transmission coefficient measurement method.

Figure 10 .
Figure 10.Comparison between experimental and simulated data.

Figure 12 .
Figure 12.The sheet resistance measurement values of the bottom passband layer for samples A and B.

Figure 13 .
Figure 13.The impact of sheet resistance manufacturing tolerance on performance.

Figure 14 .
Figure 14.The impact of interlayer misalignment on sample performance.

Table 1 .
Performance comparison of the frequency-selective absorber with wide transmission bands and other designs.