In recent years, the saturation of the wireless communication market and increase in the amount of data transit, including multimedia information, have resulted in the expansion of carrier frequencies for wireless communication into the millimeter-wave and sub-terahertz bands. Examples of this development include 5G communication, WiGig, car radar, and advanced driver assistance systems [1–3]. In particular, 5G FR2, which operates at millimeter-wave frequencies, is being continuously expanded to include new frequency ranges [4, 5]. The proliferation of wireless communication has also led to a significant increase in research on millimeter-wave absorbers as a solution for electromagnetic interference. In this context, the use of metamaterials has been evaluated as an effective means of suppressing electromagnetic interference [6].

Various studies have been conducted on absorbers equipped with metasurfaces, focusing on the choice of substrate and resistive materials as well as processes for metasurface fabrication [7–17]. Among these studies, many employed low-k foam substrates to expand the absorption band [9, 16, 17]. However, in general, the materials used for additional characteristics, such as optical transparency, mechanical strength, and mechanical flexibility, are characterized by relatively high permittivity [10–13, 15]. Notably, the use of high-permittivity substrates is known to be detrimental to the broadband performance of absorbers, particularly their oblique incidence performance [10].

Soh et al. [11] conducted one of the earliest studies on millimeter waves, which dealt with frequencies for automotive radar systems. The researchers proposed a two-layer millimeter-wave Jaumann absorber operating at the frequencies of 60 GHz and 76 GHz, consisting of two ITO films placed on polymeric substrates. Through a comparison of the design and experimental results, the researchers confirmed that the resonance frequency is very sensitive to the permittivity (or thickness) of substrates in such high-frequency applications. Singh et al. [12] presented an absorber operating at 77 GHz, achieved by forming a thin gold film on a 125-μm-thin flexible polyimide (PI) substrate and fabricating a metasurface using a standard optical photolithography process. Wang et al. [13] developed an absorber that attained an absorption performance of 90% at frequencies ranging from 65 GHz to 68 GHz, fabricated by forming a 0.1-mm-thin copper metasurface on an FR4 substrate. The aforementioned studies achieved relatively narrow absorption bandwidths at normal incidence by employing thin substrates at high frequencies. However, they did not report absorption performance under oblique incidence. Meanwhile, Wu et al. [14] presented a W-band absorber with 90% absorption performance from 73.5 GHz to 110 GHz while also reporting on its oblique incidence performance at various incident angles. The researchers fabricated a concise metal mesh using electrohydrodynamics printing technology on a 525-μm-thin PET substrate, which is expensive but favorable for ensuring good dimensional precision of metasurfaces.

Lai et al. [15] presented a transparent absorber operating below 40 GHz that comprised a metasurface formed by etching an ITO film coated on a glass substrate (ε_r ≅ 5.5). They found that oblique incidence absorption performance deteriorates significantly with an increase in oblique incidence angle. Subsequently, Liu and Kim [16] presented a broadband absorber operating below 40 GHz using low-k foam substrates and two metasurfaces printed with resistive carbon ink to achieve broadband absorption performance. Furthermore, Liu and Kim [17] presented a broadband absorber composed of three metasurfaces to extend the frequency up to 50 GHz. However, researchers [16, 17] observed that the broadband absorption performance of absorbers using low-k foam deteriorates severely at oblique incidence. This implies that broadband absorption performance at normal incidence does not necessarily guarantee an absorption bandwidth at oblique incidence. Furthermore, applying screen-printing technology that uses carbon ink, which is highly productive and inexpensive but offers relatively low printing quality compared to other processes, to absorbers operating at frequencies beyond 50 GHz [17] emerged as yet another challenge.

In this study, we present millimeter-wave absorbers for the WiGig (55–68 GHz) and 5G FR2 (n257–n261) (22–44 GHz) frequency ranges, composed of polymer substrates and metasurfaces fabricated using screen-printing techniques. The proposed absorbers achieve absorption performances better than −10 dB at normal incidence and, concurrently, better than −8 dB at 45° oblique incidence within the given frequency ranges.

Thermoplastic polyurethane (TPU), a type of thermoplastic elastomer (TPE), was employed as a flexible substrate material. Notably, TPU is considered the most representative TPE because it has excellent processability and recyclability, and above all, it has a low price. For this study, TPU substrates were manufactured into sheets of a specific thickness through a roll-forming process. Subsequently, a 0.04-mm-thick adhesive film was attached to one side of the TPU sheet through a lamination process. The thickness of the TPU sheet was determined based on the absorber design results. The printing substrate used for the screen-printing process was a PI film with a thickness of 0.05 mm. The material used as the PEC ground was a thin copper film with a 0.02-mm adhesive film attached to one side.

The permittivity of the TPU was estimated from the S-parameters measured using network equipment consisting of a Keysight N5227B PNA equipped with a Keysight N1500A, a N5292A millimeter-wave test controller, N5295AX03 120 GHz frequency extenders, and free space measurement equipment (FS-110; EM Labs, Kobe, Japan). Fig. 1 shows a photograph of the equipment used for measuring normal and oblique incidence. Fig. 2 shows the measured complex permittivity of the TPU from 18 GHz to 110 GHz, indicating a nearly constant value across the entire frequency range, with the average value being ɛ_r=3.098 – j0.1256.

The metasurfaces were fabricated onto a 50-μm-thick PI film using resistive ink in a square-loop pattern. Fig. 3 shows the shape and dimensional parameters of the square-loop pattern constituting the metasurfaces of the absorbers.

Kim et al. [10] reported that the cross-sectional shape and coating thickness of circuits produced by screen-printing technology are highly irregular. This observation led them to calculate the effective sheet resistance Rs of printed circuits from the measured line resistance. Figs. 4 and 5 present close-up images, 3D profiles, and 2D cross-sections of the square-loop patterns printed with circuit linewidths (w) of 0.15 mm and 0.25 mm, respectively. The printed materials presented in Figs. 4 and 5 were produced using the same printing equipment and printing environment, maintaining identical specifications for the screen mask and resistive ink. However, due to the difference in circuit linewidths, the coating thickness exhibits a nearly twofold difference.

While the effective sheet resistance of conductive ink is influenced by factors such as heat treatment temperature and duration [10], it was inferred that the effective sheet resistance Rs of the two patterns would differ approximately twofold when accounting for the impact of coating thickness.

Fig. 6 shows the schematic configuration of the designed absorbers, where H₁ and H₂ indicate the summations of thicknesses of the TPU substrate and other film-like materials.

Since the actual laminated structures used in the absorbers were quite complex, in the absorber design stage, the design model was simplified by assuming that the complex permittivity of the adhesive and PI films are the same as that of TPU. Fig. 7 depicts the equivalent circuit of the absorbers with the proposed simplified laminated structure. Notably, since the single-layer absorber and double-layer absorber presented in Fig. 6 both feature a dielectric substrate over the metasurface, they can be expressed using one identical equivalent circuit, as shown in Fig. 7.

To determine the metasurface design parameters, including thicknesses H₁ and H₂, sheet resistance Rs, and dimensions D, w, and g, satisfying the required absorption performance in the given frequency range, a full-wave computational electromagnetic (CEM) technique was implemented using the unit-cell model in CST Studio Suite. The design process involved selecting the design result demonstrating an absorption performance better than −8 dB at 45° oblique incidence from the design results that satisfied the absorption performance of −10 dB at normal incidence within the frequency range of interest.

Fig. 6(a) illustrates the design of the WiGig absorber. Notably, fractional bandwidth is defined as the ratio of the absorption bandwidth to the center frequency. The fractional bandwidth required for a WiGig absorber is considerably narrower than that for single-layer absorbers presented in previous studies [9, 10]. Along these lines, Fig. 8 compares the absorption performance of a WiGig absorber designed to exhibit broadband absorption performance at normal incidence (WG-1) to that of the design proposed in this study (WG-2) at normal and oblique incidences. Table 1 presents the parameters of the two designs.

In Table 1, H₁ was determined when f_r was 60 GHz, which is the center frequency of WiGig, using Eq. (1):

Here, c refers to the speed of light in vacuum and ε_r indicates the permittivity of the substrate in Fig. 2. Fig. 8 shows that the normal incidence wave absorption performance of WG-1 is excellent, but its TM mode oblique incidence performance is not good. This trend is consistent with the research results of Kim et al. [10], who found that the large metasurface periodicity of microwave absorbers composed of a highly dielectric substrate is disadvantageous in achieving good oblique incidence performance. The degradation of the oblique incidence performance of absorbers with large metasurface periodicity has also been observed by Liu and Kim [16, 17]. In contrast, Fig. 8 confirms that WG-2 achieved narrowband characteristics along with only one absorption peak instead of the two absorption peaks commonly observed for single-layer broadband absorbers [9, 10]. This design was derived for the purpose of reducing metasurface periodicity while maintaining a thin circuit linewidth to attain sufficient absorption performance under oblique incidence [10].

Compared to WiGig absorbers, the fractional bandwidth required for 5G absorbers is relatively wide. For a comparative study, two 5G absorbers were designed—5G-1, presented in Fig. 6(a), and 5G-2, depicted in Fig. 6(b)—with a fixed circuit linewidth w of 0.25 mm. Their absorption performances are illustrated in Fig. 9, and their design parameters are presented in Table 2. It is observed that the absorption performance of 5G-1 is degraded at oblique incidence, similar to the absorption performance of WG-1 in Fig. 8. In contrast, since 5G-2 is characterized by reduced metasurface periodicity along with an additional TPU substrate on the metasurface, as shown in Fig. 6(b), it exhibits better absorption performance at oblique incidence compared to 5G-1 [10, 18].

It should be noted that, as described in Eq. (2), the ratio of the difference in sheet resistance Rs (Ω/sq) of the metasurfaces used in WG-2 and 5G-2 was similar to the ratio of the reciprocal values of the coating thicknesses between Figs. 4 and 5.

Here, R indicates the resistivity (Ω·mm) of resistive ink and t refers to the coating thickness (mm).

The fabricated millimeter-wave absorbers presented in Fig. 10 were attached to 10-mm-thick polystyrene foam plates for handling, ensuring flexibility of the absorbers during measurement. In particular, WG-2 (w = 0.15 mm, Rs = 45 Ω/sq) and 5G-2 (w = 0.25 mm, Rs = 24 Ω/sq) were fabricated. As shown in Fig. 6(a) and 6(b), WG-2 and 5G-2 were manufactured by bonding a thin copper film, a TPU substrate, and a PI film using adhesive films.

All verification specimens were fabricated by conducting simple manual adhesion processes. To manufacture WG-2, a PI film with the metasurface printed on it was placed on the floor with the printed side facing upward, following which a 0.65-mm-thick TPU sheet with an adhesive film attached to one side was laminated on top of it. The film and the sheet were then pressed to adhere them together. Subsequently, a thin copper film with an adhesive film attached to one side was laminated on the top surface of the TPU sheet and then pressed to ensure adhesion. 5G-2 was manufactured in a similar manner to that of WG-2 by first placing a 0.65-mm-thick TPU sheet on the floor with its adhesive film side facing upward, and sequentially laminating a PI film, a 0.91-mm-thick TPU sheet, and a thin copper film thereafter.

The performances of the absorbers were measured based on their scattering parameters using the same equipment employed to measure the permittivity of the materials, as shown in Fig. 1.

Fig. 11 compares the calculated and measured absorption performances of WG-2. Notably, the absorption performance was recalculated by accounting for the increase in thickness resulting from the adhesive parts of the fabricated absorber—H₁, which includes the two adhesive parts, increased from 0.71 mm to 0.74 mm. The calculated absorption performance under normal incidence conditions attained a peak at a frequency of about 50 GHz, which is close to the peak of the measured absorption performance. The large peak shift in the calculated absorption performance in Fig. 11 for WG-2 from that in Fig. 8 can be attributed to the high dimensional sensitivity at high-frequency bands, i.e., the very short wavelength of millimeter waves. As evident from Eq. (3), which is simply derived from Eq. (1), a frequency shift of around 3 GHz occurs when the substrate thickness d increases by only 0.03 mm in the calculation for Fig. 11 from the original thickness of 0.71 mm considered for WG-2.

Here, f refers to frequency (mm). Therefore, it is obvious that the irregular printing quality of the metasurface affects the absorber’s performance. Nevertheless, due to the sufficient design margin of WG-2, excellent absorption performance, with values exceeding −10 dB, was achieved within the frequency range of interest (55–68 GHz) for both normal and 45° oblique incidences.

Fig. 12 compares the calculated and measured absorption performances of 5G-2. Similar to the case of the WiGig absorbers, the absorption performance was recalculated by reflecting the increase in thickness of the adhesive parts in the fabricated absorber—H₁ and H₂ were adjusted to 1.03 mm and 0.77 mm, respectively. Although the measurement results of 5G-2 differ slightly from the calculated results, Fig. 12 verifies that the fabricated absorber achieved excellent absorption performance at both normal incidence and 45° oblique incidence between 22 GHz and 44 GHz, which is the frequency range of interest for the 5G absorbers considered in this study.

The differences between the calculated and measured results in Figs. 11 and 12 may have naturally been caused by measurement and manufacturing errors in the thickness and permittivity of various materials constituting the substrate [11]. However, it must be noted that the non-uniform cross-sectional shape of the printed lines, as observed in Figs. 4 and 5, as well as the resulting irregularity in sheet resistance and linewidth, can also be considered significant causes of the discrepancy between the calculated and measured results [10].

Table 3 compares the performance of the WiGig and 5G absorbers developed in this study with that of existing absorbers. The fractional bandwidths at normal incidence correspond to the −10 dB absorbing bandwidth divided by the center frequency of the bandwidth. Likewise, fractional bandwidths under oblique incidence correspond to the −8 dB absorbing bandwidth. The thickness of the absorbers is presented as a ratio to wavelength λ_L corresponding to the lower frequency bound of the −10 dB absorbing bandwidth at normal incidence. Table 3 shows that the absorbers proposed in this study maintain excellent absorption bandwidths at both vertical and oblique incidences compared to those reported in previous studies, especially considering their relative thicknesses (unit: λ_L), thus verifying their performance

In this study, millimeter-wave absorbers for the WiGig and 5G FR2 (n257 to n261) bands are proposed. The absorbers are composed of a TPU substrate (|ε_r | ≅ 3.1), a type of flexible material, and a square-loop type metasurface. The absorber for WiGig application was designed to secure a reflection loss of more than −10 dB at normal incidence and more than −8 dB at 45-degree oblique incidence within the 55 GHz to 68 GHz frequency band. Likewise, the absorber for 5G FR2 was designed to achieve the same reflection losses within the frequency band ranging from 22 GHz to 44 GHz.

This study establishes that absorbers designed for broadband absorption at normal incidence are not necessarily advantageous for oblique incidence absorption. In addition, this study introduces a design plan to successfully achieve oblique incidence absorption bandwidth by slightly sacrificing the normal incidence absorption bandwidth or slightly increasing the absorber thickness.

The metasurface was fabricated using resistive ink on PI film using a screen-printing technique that is easy to mass-produce. However, it was observed that the quality of the printed circuit of the square-loop metasurface fabricated using this technique was uneven. Moreover, the coating thickness of the resistive ink was affected by the circuit linewidth, which in turn affected the effective sheet resistance of the printed matter. Nonetheless, the absorbers constructed for the two frequency ranges were successfully designed using the same printing material and process by accounting for the difference in sheet resistance according to linewidth. The measured absorption performances of the absorbers demonstrate that screen printing is feasible in the WiGig and 5G FR2 millimeter-wave bands.