The square structure of metal mesh (MM) is selected due to its high flexibility, compactness, lightweight properties, transparency, and mechanical robustness [7]. Fig. 1 shows the dimensions (L × L) of the MMF structure. As shown in Fig. 1(a), MM is produced with a square lattice of horizontal and vertical copper strip lines on a polyethylene terephthalate (PET) substrate. The metal mesh and transparent PET layers are 2 μm and 100 μm thick, respectively. The unit cell of the MMF structure is depicted in Fig. 1(b). Copper strip lines of a certain width (w) are arranged between spaces (s) in a regular pattern and cross each other. In this way, by using the MMF, visible light can easily flow through, while the copper conductive component maintains its high conductivity.

The ratio between the non-metalized strip lines and the total area is used to determine the theoretical transparency of the MMF, which are both formed from the mesh width (w) and mesh spacing (s) of the MMF structure. In [11], the average optical transparency (OT_av) of MMF was determined via

where OT_PET is the average optical transparency of the PET substrate and exceeds 90% [11].

Fig. 2 shows the OT_av the curve of the MMF. Here, w ranges from 5 to 50 μm, whereas s varies from 100 to 400 μm. When s is increased, OT_av increases, and when w is increased, OT_av decreases. This trend makes sense because a decrease in w and an increase in s result in a higher ratio of light-to-pass area, and hence an increase in the transparency of the MMF. It has been noted that there is a trade-off between transparency and conductivity in the MMF [8]: conductivity affects the performance of the antenna [6, 20, 22]. Therefore, to maintain a high level of transparency, conductivity, and possible fabrication, the mesh width, mesh space, and thickness of the MM are optimized at 21 μm, 234 μm, and 2 μm, respectively.

As seen in Eq. (1), the transparency of the MMF was calculated and found to be approximately 75.7%. However, the measured results show that the OT_av of the MMF slightly decreases compared to the calculated value, with the OT_av being 69%. The OT_av of the MMF was determined using a UV-visible spectrophotometer (T60 model). As reported in the study [11], the electrical conductivity of the MMF was determined using sheet resistance. Therefore, both the calculated and measured values are in good agreement with the average sheet resistance level of 0.1Ω/sq.

Figs. 3(a) and 3(b) show the geometry of the proposed patch antenna. The proposed antenna design follows that of a conventional coaxial patch antenna, as reported in [23]. A PVC substrate (relative permittivity constant of ɛ_r= 2.7, loss tangent of tan δ= 0.022, and dimensions of W_s × L_s = 50 × 50 mm²) is used for the proposed antenna. The bandwidth of patch antennas is affected by the thickness of the substrate. To ensure that the antenna remained flexible, we used an optimized PVC thickness (h) of 2 mm. The radiator and ground components use thin MMF. The ground component covers the entire side of the PVC substrate. Table 1 shows the dimensions of the proposed antenna. The dimensions of the radiator component tapped on the other side of the substrate, are W_p × L_p = 26 × 28.5 mm². Accordingly, the antenna has two edges that open into a rectangular groove with a width and length of W_a × L_a = 6.6 × 5.7 mm², giving the proposed antenna a fundamental resonant frequency of 2.45 GHz. The feed point uses a coaxial probe with an input impedance of 50 Ω. This point has distances to the edge of the patch and substrate of L_p1=10.7 mm and L_p2= 20.45 mm, respectively.

The simulated and measured reflection coefficients (S₁₁ ) and the gain-total radiation efficiency of the transparent patch antennas are shown in Fig. 4. In Fig. 4(a), the reflection coefficient is measured using a vector network analyzer. The simulation result S₁₁ shows relatively good agreement with the measurement result, showing below −6 dB (VSWR 3:1) with operating frequency ranges of 2.4–2.51 and 5.87–7.04 GHz. The measured and simulated results of the proposed patch antenna differ slightly due to imperfect fabrication.

Fig. 4(b) shows the gain and efficiency outcomes when measured in an anechoic chamber. The proposed antenna shows a measured peak gain that exceeds 5.4 dBi (average value of 5.28 dBi) and radiation efficiency of up to 67.8% at low frequencies. In the entire high-frequency band, the maximum gain of 6.3 dBi (average value of 5.52 dBi) achieves a radiation efficiency exceeding 70%. It should be noted that the conductor loss, substrate loss, and subminiature version A (SMA) connector loss were not analyzed in the EM simulation and could have led to errors. Simulation results of the surface current distributions J [A/m] at phase zero (ϕ = 0°) of the antenna in both resonant frequencies (2.45 and 6.5 GHz) are shown in Fig. 5. From Fig. 5(a), when the patch operates in the 2.45 GHz band along the y-axis, the maximum current intensity is uniformly distributed from the probe to the edges and in phase. Thus, at 2.45 GHz, the patch antenna mainly works in the first-order mode [24]. Obviously, in this case, the outer edge of the antenna (along the y-direction) is the main component affecting the fundamental resonant frequency. In Fig. 5(b), at 6.5 GHz, there is a null current (close to the center of the antenna); hence, the corresponding radiated fields cancel each other out. Meanwhile, the resonant frequency is maintained by the current in the outer edges of the antenna along the y-axis.

In Figs. 6(a)–(b), the simulated and measured co- and cross-polarized radiation patterns on the yz- and xy-planes are investigated at the center frequency. As expected, when co-polarized, the patch antenna behaves as a directional antenna on the yz-plane but exhibits nearly an omnidirectional pattern on the xy-plane. The antenna generates a directional pattern with the peak amplitude of the main lobe at 0° and 33° at 2.45 and 6.5 GHz, respectively. In addition, the measurement of the cross-polarized value was −15 to −34 dB on the yz-plane, whereas the cross-polarized value on the xy-plane was −12 to −30 dB for the whole application band. These co- and cross-polarized results confirm the validity of the proposed antenna.

Fig. 7(a) shows the measurement setup of the fabricated antenna in an anechoic chamber with a mobile antenna measurement system (0.7–8 GHz) located at the Korea Radio Promotion Association.

The far-field pattern measurement method was used to calculate the gain and total efficiency of the antenna under test (AUT) [25]. The AUT was placed at one end of the chamber acting as a receiving antenna, the source antenna was placed at the other end as a transmitting antenna. Then, the results were analyzed via vector network analysis. In Fig. 7(b), the fabricated antenna shows transparency over text. Because of the onset temperature of MMF melting at approximately 150°C, we used a silver paste liquid (Elcoat P-100) to connect the probe feed to the feed point of the proposed antenna. As shown in Fig. 7(b), the OT_av of the antenna slightly de creased (OT_av ≈ 42.8%) when looking through the radiator as compared to its outer part (OT_av ≈ 62%). Fig. 7(c) outlines the bending conditions of the antenna, indicating that it is flexible.

Bending tests are applied to ensure practical operability, given that the antenna is anticipated to be bent and rolled when incorporated into flexible electronic devices. The antenna under test (AUT) was conformed to foam (ɛ_r=1) with two radii, R₁ = 25 mm and R₂ = 40 mm, to test its performance under different states of bending, as shown in Fig. 8. In Fig. 8, the measured reflection coefficient remains below −6 dB in the Wi-Fi 6E frequency range. The bandwidths of the AUT in the R₁ configuration are 2.4–2.51 GHz (at 0.11 GHz, 4.5%) and 6.02–7.02 GHz (at 1 GHz, 15.3%), while the resonant band of the R₂ configuration is much better, from 2.39–2.52 GHz (at 0.13 GHz, 5.2%) and 5.91–7 GHz (at 1.09 GHz, 16.8%). These results show that the resonant frequency characteristics of the AUTs tend to move slightly to the right side compared to the planar condition, and the bandwidth becomes smaller because of bending.

Figs. 9(a) and 9(b) reveal the impact of bending on the radiation pattern at the center frequencies of 2.45 GHz and 6.5 GHz. Overall, the AUT maintained its directional radiation pattern while conforming to the foam. The measurement gains achieved with bent conditions R₁ and R₂ at 2.45 GHz were 4.3 dBi and 3.3 dBi, while at 6.5 GHz they were 5.3 dBi and 5.5 dBi, respectively. In addition, at 2.45 GHz, the measuring total efficiency with bending conditions R₁ and R₂ were 65% and 60%, respectively, whereas at 6.5 GHz, they were 67.2% and 68.2%, respectively. Due to the bending effect, the AUTs had slightly decreased gain compared to the planar condition. The antenna bending on foam with R₁ was impacted most by the highest bending level of 25 mm. In low frequency, this makes the antenna more directional; therefore, the gain of bending with R₁ increases than R₂, as shown in Fig. 9(a). The measured radiation efficiency of the antenna showed slight differences between bending with R₁ and R₂. This effect can be attributed to additional radiation loss caused by imperfections in measurement and fabrication.

The AUT was conformed to a lamp as an example to assess its applicability in smart home applications, as shown in Fig. 10, in which the lamp is bent by nylon (ɛ_r=4.5), showing a radius of R₃ = 75 mm. The measured fundamental frequency is maintained at 2.39–2.5 GHz. In the high-frequency range (6.15–7.15 GHz), the measured bandwidth moved slightly to the right side compared to the planar condition. This can be explained by the bending and dielectric effects of the lamp. The external material (nylon) is placed very close to the antenna. Furthermore, the electric field lines of the antenna can be influenced by the material, leading to additional capacitance or inductance, which can affect the impedance of the antenna. The flexibility test setup and measurement result (S₁₁) for the dual-band antenna conformed to a lamp is shown in Fig. 10(b).

Figs. 11(a) and 11(b) show the simulated 3D radiation patterns of the proposed antenna at 2.45 GHz and 6.5 GHz, respectively. In this case, the simulated results for the AUT show a peak gain of more than 3.9 dBi, corresponding to a radiation efficiency of approximately 63% at a low frequency. Over the entire high-frequency band, the highest gain of 5.4 dBi provides a radiation efficiency of more than 68%. The radiation efficiencies show slight differences when compared to the planar condition (in low and high frequencies, the differences are less than 4% and 2%, respectively). It makes the AUT suitable for applications that require highly directional antennas.

Table 2 shows the performance comparison of the planar and flexible conditions of the proposed antenna. The lamp is made of nylon and affects the radiated efficiency of the antenna due to the interaction of the radiation field with the material. However, the thickness of the nylon is relatively thin since it is not significantly affected when compared to the bend on foam. These results show that the proposed antenna has acceptable performance and has the potential to be used in flexible IoT applications.

Table 3 provides a performance comparison between the proposed antenna and existing state-of-the-art T&F patch antenna structures. From this comparison, the proposed antenna was optimized for gain and efficiency compared to previous reports. In addition, the possibility of integrating antennas into glass, plastic, wood, or other common home surfaces is also examined in terms of IoT applications. This problem will be carefully investigated in future work.