Millimeter waves, which are the frequencies used in 5G, have shorter wavelengths than lower frequency signals. These waves tend to be more sensitive to obstacles, including glass windows [19]. The type of glass used in windows, such as conventional glass, coated glass, or specialized materials (low-emissivity glass), can affect how millimeter wave signals interact with the surface. The effect of window glass on 5G millimeter wave signals must be carefully considered during the design process, as shown in Fig. 2.

In the simulation, two Floquet ports were used based on boundary conditions to excite the structure with incident wave angles of TE 0°. The considered glass had a variable dielectric constant (3, 5, 7.38, and 9) and variable thickness (2–6 mm). In most cases, increasing the dielectric constant or thickness of the glass material resulted in a higher transmission loss. The loss was primarily due to dielectric absorption, which is a process in which the dielectric material absorbs and then re-emits energy or in which signals must traverse a longer distance through the dielectric material, leading to signal attenuation. Additionally, low penetration loss glasses have low dielectric losses, resulting in less effect on transmission than high penetration loss glasses [27].

The primary distinction between the two FSSs lies in their substrates. As shown in Fig. 3(a), GPTS-1 utilized borosilicate glass, a low-loss substrate with a thickness of 3.3 mm and a dielectric constant (ɛ_r) and a loss tangent (tanδ) of 4.6 and 0.0037, respectively. In contrast, GPTS-2 employed conventional glass, a high-loss substrate (ɛ_r = 7.38, tanδ=0.06) with a thickness of 3 mm, as shown in Fig. 3(b). This difference in substrate properties had a significant impact on the characteristics and performance of the respective FSSs. The metal lines on both FSSs were made of copper with a thickness of 35 μm. These metal lines were printed on an ultra-thin polyethylene terephthalate (PET) film (ɛ_r = 3.5, tanδ=0.022), which had a thickness of 100 μm.

The dimension of the aperture dipole (L) was initially determined by [28] as follows:

where L represents the slot lengths (d₂), s represents the slot widths, ɛ_a is the effective dielectric permittivity (ɛ_a = ɛ₀ +ɛ_r)/2, ɛ₀ is the dielectric constant of the outermost layer (e.g., air), and f_c is the resonant frequency at 28 GHz. Compared to glass, PET is very thin. Therefore, the value of ɛ_r of PET was equal to the value ɛ_r of glass.

The dimensions of the two FSSs based on a periodic unit structure were then optimized in a simulation conducted using CST software. As shown in Fig. 4(a), if the incident wave was polarized perpendicular to the narrow strips, leading to the accumulation of positive and negative charges on the lower and upper strips, respectively, the shunt impedance became capacitance (C) [22, 23]. In addition, when the incident wave was polarized parallel to the strips, the shunt impedance became impedance (L). Here, L is equal to the sum of the values of L₁ and L₂. Evidently, the current length of L₁ was significantly shorter than that of L₂, resulting in an inductance value L₁ ≪ L₂. For rough estimates or a first-order approximation of capacitance (C), we can ignore inductance L₁. The effective capacitance and inductance values can be calculated in accordance with [24, 25]. By combining capacitive and inductive elements within a compact structure, as shown in Fig. 4(b), the resonant frequencies (f_c) were expressed as follows:

Fig. 5 compares the simulated transmission coefficients between the full-wave EM and the ECM, showing comparable shapes in the transmission responses of both FSSs. FSS-1 and FSS-2 without glass showed almost no reflection at 36 GHz and 39 GHz, respectively. By applying FSSs onto glass, it became evident that glass affects transmission and reduces transmission ability.

Since both GPTSs had the same ECM, to enhance the Q-factor and transmission, the key parameters associated with GPTS-1 were investigated, as illustrated in Fig. 6. Fig. 6(a) shows that the Q-factor increased as the capacitance value (C₁) increased and that this occurred concurrently with a decrease in the distance between the two microstrip lines (s) [25]. As shown in Fig. 6(b), an increase in the Q-factor was observed when the inductance values (L₂) decreased in correspondence with an increase in the width of the line (w) [25]. L₂ induced a transmission zero at around 33 GHz, and the L₂ value decreased, the frequency of this transmission zero correspondingly increased.

In addition, as the dielectric constant of glass decreased, not only did the Q-factor increase, but the transmission was also enhanced, as shown in Fig. 6(c). This demonstrates that the penetration loss of the substrate had a significant effect on transmission. Fig. 6(d) shows that a transmission peak of less than 12 dB occurred at approximately 10.6 GHz. This phenomenon occurred because the thickness of the glass altered the propagation characteristics of EM waves through the material

Based on the above analysis and the results in Fig. 2, the easiest way to improve transmission is to choose a substrate with a low penetration loss (e.g., borosilicate glass for GPTS-1). However, for conventionally available glass windows, such as GPTS-2, which have a high penetration loss, there is an approach that can enhance transmission by incorporating an additional dielectric substrate.

Fig. 7(a) shows that, in the case of GPTS-1, when only the metal line width (w) increased, a constant total area for the unit cell was maintained, and the transmission response in the out-of-band signal typically decreased. This was similar to the results for GPTS-2. In addition, we investigated how the width of the metal line affected both the metal area and the transparency of the two FSSs, as shown in Fig. 7(b). The transparency of the FSS can be calculated as the percentage of light passing (without metal) per the total area of the unit cell [14, 29, 30]. As the metal line width (w) increases, there is an accompanying rise in the metal area, leading to a decrease in the optical transparency (OT). In the present study, opting for a narrow metal line width (100 μm) led to excellent transparency, with FSS-1 of 76% and FSS-2 of 79%. However, it is also crucial to address the challenge of minimizing fabrication costs while attaining the desired transparency. We aimed to improve transmission for frequency filtering at 28 GHz over glass windows using inexpensive dielectric slabs instead of multilayer FSSs, which are costly and complex [7–9]. Therefore, a metal line width of 200 μm was chosen, and the moderate OT values were 57% for FSS-1 and 62% for FSS-2. The flexible application of FSS on glass with multimode windows (Fig. 1) did not significantly affect the aesthetics or transparency of the glass window.

The utilization of matching and propagation matrices offers a straightforward approach for addressing various interface problems. As shown in Fig. 8, we focused on scenarios involving uniform plane waves that are normally incident on material interfaces. The two-interface problem in Fig. 8(a) depicts a dielectric slab η₁ dividing the semi-infinite media η_a and η_b from one another. The slab had a width of l₁, a refractive index of n₁, a propagation wave number k₁ = ω/c₁, and a wavelength within the slab λ₁ = 2π/k₁ = λ₁/n₁. Additionally, λ_a was the wavelength inside the medium η_a. We assumed that the incoming wave went from the left medium η_a through slab η₁ and exited medium η_b. Based on [21–23], the reflection coefficient (Γ₁) of medium η_a was written as follows:

where the two-way travel time delay in the z-domain is denoted as z⁻¹ = e^−jωT = e^{−2jk₁l₁}, and ρ₁, ρ₂ are the elementary reflection coefficients from two interfaces corresponding to the following:

To enhance transmission from medium η_a to η_bor η₁, a reflectionless interface corresponding to Eq. (3) must be equal to zero, which occurs when ρ₁ + ρ₂z⁻¹ = 0. This led to two cases. Case 1 was expressed as follows:

which translated into the half-wavelength condition of l₁ = mλ₁/2, which was based on Eq. (4), and corresponded to η_a = η_b.

Case 2 was expressed as follows:

This provided the quarter-wavelength condition l₁= (2m + 1)λ₁/4, used Eq. (4), and correspond to η12=ηaηb.

From Eq. (5), the following reflection coefficient (Γ₁) for the half-wavelength case was obtained:

Similarly, for Eq. (6), the reflection coefficient (Γ₁) for the quarter-wavelength case was given as follows [21–23]:

As shown in Fig. 8(b), if the left side of the slab was air, the right side was glass (ɛ_r = 7.38, n = 1.5), and there was no backward-moving wave in the rightmost medium (Γ3 = 0), the scenario depicted in Fig. 8(a) occurred. We used Eq. (8) so that there was no reflection and chose a dielectric slab made of polyvinyl chloride (PVC) (ɛ_r = 2.8, tanδ = 0.022, and n = 1.53). The quarter-wavelength thickness of PVC at 28 GHz was calculated to be 1.5 mm. Therefore, the reflection coefficient was approximately 0.03.

However, as shown in Fig. 8(b), assuming that Γ₃ ≠ 0, the addition of a dielectric slab on the right side of the glass was necessary to prevent reflections at the glass layer (Fig. 8(c)). In this case, the reflection coefficient (Γ₃) was written as follows:

For the anti-reflection, the chosen thickness and permittivity of the dielectric slab were similar to the case shown in Fig. 8(b).

By varying the dielectric constant of the glass according to Eq. (8), the values of the quarter-wavelength-thick dielectric slabs were calculated. In Fig. 9(a), using a 3 mm-thick glass, the values of the dielectric slab based on Eq. (8) were 2.32 (slab-1), 2.52 (slab-2), and 2.72 (slab-3) when the dielectric constant changed to 5.38 (glass-1), 6.38 (glass-2), and 7.38 (glass-3), respectively. The simulation results for transmission showed improvements of 1.7 dB, 2.03 dB, and 2.2 dB without/with a dielectric slab corresponding to glass-1, glass-2, and glass-3, respectively.

To confirm the theory and simulation, measurement results were studied for the conventional glass (3 mm thick and ɛ_r = 7.38) without/with a dielectric slab of PVC (1.5 mm thick and ɛ_r = 2.8), as illustrated in Fig. 9(b). The measurement results for the glass were better than the simulation results. The reason for this discrepancy could be related to the EM properties of the glass at the specified frequency, including its dielectric constant or refractive index. Here are some potential reasons why this might have occurred:

1) Inaccurate material models: Simulations based on mathematical models to describe the EM properties of materials, including their dielectric constants and thicknesses. Material models are often approximations and might not capture all the nuances of glass behavior, especially at specific frequencies.

2) Frequency-dependent behavior: Glass exhibits frequency-dependent behavior that was not adequately accounted for in the simulation. In the simulation, the dielectric constant measured up to 1 GHz and had an average value of 7.38, and a loss tangent of 0.06 was used for the simulation at the full frequency range.

3) Differences arose because of unavoidable experimental errors, in which power was excited and received by real horns instead of the waveguide port in CST. Additionally, the measurement setup, calibration, and environmental conditions could have introduced uncertainties.

At 28 GHz, the transmission results (glass + slab) increased by 2.2 dB in the simulation and by 1.52 dB in the measurement when compared to the case without a slab. When two slabs adhere to the glass (slab + glass + slab), this configuration resembles a sandwich with glass in the middle. Compared to the case with glass only, at 28 GHz, the transmission showed a 3.2 dB improvement in the simulation and a 2.38 dB increase in the measurement.

Fig. 11(a) and 11(b) show the simulated and measured transmission coefficients of GPTS-1 with incident wave angles of 0° and 30°, respectively. The measurement results revealed a slight right shift compared to the simulation, possibly due to imperfections in adhering the FSS to the glass. The transparent adhesive was omitted from the simulation. Borosilicate glass has a low-loss substrate, resulting in its 28 GHz insertion loss value outperforming that of conventional glass in the measurements and simulations by approximately 1.7 dB. For the normal incidence waves, the measurement results for GPTS-1 showed a 3 dB transmission bandwidth extending from 26 to 31.5 GHz and a maximum insertion loss of 1.4 dB at 28.4 GHz. While the transmission of GPTS-1 did not reveal a significant improvement compared to glass, it was evident that it effectively blocked the out-of-band frequency. This contributes to an overall enhancement in transmission speed and a significant reduction in potential issues that can affect data transfer [1]. Fig. 11(b) illustrates the TE mode at a 30° incident angle, revealing a maximum frequency deviation of 3%, while the TM mode exhibited a deviation of 1.7%. The 3 dB transmission bandwidths of the TE/TM modes were 26.2–29.44 GHz/25.8–28.56 GHz.

Fig. 12 shows the simulated and measured transmission coefficients for GPTS-2 without/with dielectric slabs. For GPTS- 2/Slab (Fig. 12(a)), the slab was placed on the opposite side of the FSS-2 through the glass. In the case of the two slabs adhering to GPTS-2, this configuration resembled a sandwich with GPTS-2 in the middle, as shown in Fig. 12(b).

As shown in Fig. 13(a) and 13(b), when there was no dielectric slab (GPTS-2 only), the simulation and measurement results both indicated that the transmission bandwidths were lower than 3 dB. Fig. 5 clearly depicts the impact of glass on GPTS transmission. Borosilicate glass (low penetration losses) and GPTS-1 both had better transmission results (>–3 dB) than conventional glass (high penetration losses) and GPTS-2.

To improve transmission, we proposed using a dielectric slab, as discussed in Section III. When a dielectric slab was present (GPTS-2/Slab), the simulated transmission results improved by 1.84 dB at 28 GHz, while the measured transmission results exhibited a 1.7 dB enhancement at 30 GHz.

The measurement results showed a 3 dB transmission bandwidth extending from 28 to 31 GHz. Additionally, when using two dielectric slabs (Slab/GPTS-2/Slab), the measured transmission results exhibited a 1.08 dB enhancement at 27.16 GHz and a 3 dB transmission bandwidth from 23.36 to 29.24 GHz. In this case, the transmission bandwidth shifted toward lower frequencies, which can be explained based on Eq. (1).

In Fig. 13(c), the GPTS-2/Slab configuration showed 3 dB transmission bandwidths of 28.84–30.6 GHz and 27.44–29.6 GHz for the TE/TM modes at a 30° incident angle, with maximum transmission coefficients of 2.15 dB/2.2 dB. In Fig. 13(d), the Slab/GPTS-2/Slab configuration revealed 3 dB transmission bandwidths of 23.24-29.2 GHz and 23.12–28.48 GHz for the TE/TM modes at a 30° incident angle, with maximum transmission coefficients of 1.27 dB/1.18 dB.

Notably, the measurement results for the transmission of glass were better than the simulation results, as explained in Section III-2. This led to differences in the measured transmission results for GPTS-2 with and without a dielectric slab. A slight rightward frequency shift occurred because of imperfections in the adhesion of the FSS onto the glass, resulting in the formation of small air gaps.

Table 1 presents a comparison of our proposed FSS and recent designs with similar applications. The analysis highlights that our designs in having the narrowest 3 dB fractional bandwidth (FBW), minimal transmission loss, satisfactory OT, and a lower fabrication cost compared to metal mesh or metal coating. Notably, our work, with its crucial window glass thickness for stability in this application, has proven to be more suitable for building use than the methods outlined in prior studies [9, 10, 13]. For the incident angle, when TE polarization was considered, the incident angle increased, and wave impedance (Z_TE = Z₀/cos(θ)) increased, whereas glass impedance (Z_S) remained constant [31]. This caused an impedance mismatch between the incident wave and the glass, resulting in a higher transmission loss.