Feed

In the design of transmitarrays, the effective utilization of the radiation field of a feeding antenna to generate coherent interference is crucial. The choice of a feed antenna often involves selecting one with a high front-to-back ratio (FBR) to avoid backward radiation. Figure 1 shows the quasi-Yagi antenna serving as the feed, fabricating on a 0.2 mm thick Rogers RO4003 substrate with a relative permittivity (ε_r) of 3.55. In simulated patterns at 28 GHz, the quasi-Yagi antenna exhibits an FBR value of 20.2 dB, indicating a high FBR suitable for the transmitarray. The antenna also demonstrates a bandwidth of 22.1%, covering 25.53–31.54 GHz. The E-plane and H-plane radiation patterns at 28 GHz indicate half-power beam widths (HPBWs) of 57° and 113°, respectively.

Figure 1. Geometry of the feeding quasi-Yagi antenna (unit: mm).

Investigating the HPBWs of the feed antenna holds paramount importance in the design of transmitarrays, influencing the focal distance (f) and subsequently governing the focal length to diameter ratio (f/D). The f/D plays a crucial role in determining how effectively the radiation pattern of the feed antenna illuminates the entire aperture of the transmitarray. In our optimization strategy, we employ the power of cosine functions cos^q(θ) to fit the radiation patterns for both E-plane and H-plane, where q represents the power. The quasi-Yagi antenna introduces nonsymmetric radiation patterns in both planes. By determining the optimum q for both planes, we can calculate the illumination efficiency (η_i), spillover efficiency (η_s), and total efficiency (η_t). These efficiencies are expressed as follows:

(1)\begin{equation}{\eta _i} = \frac{{{{\left\{ {\frac{{\left[ {\left( {1 - {\text{co}}{{\text{s}}^{q + 1}}{\theta _e}} \right)} \right]}}{{\left( {q + 1} \right)}} + \frac{{\left[ {\left( {1 - {\text{co}}{{\text{s}}^q}{\theta _e}} \right)} \right]}}{q}} \right\}}^2}}}{{2{\text{ta}}{{\text{n}}^2}{\theta _e}{ }\left[ {\frac{{\left( {1 - {\text{co}}{{\text{s}}^{2q + 1}}{\theta _e}} \right)}}{{\left( {2q + 1} \right)}}} \right]{ }}}\end{equation}

(2)\begin{equation}{\eta _s} = 1 - co{s^{2q + 1}}{\theta _e}\end{equation}

(3)\begin{equation}{\eta _t} = {\eta _i} \times {\eta _s}\end{equation}

The evaluation of these efficiencies at different f/D values is instrumental in optimizing the design and maximizing the utilization of both the radiation pattern of the feed and the transmitarray aperture. Figure 2 illustrates the results for the E-plane and H-plane, showcasing the trade-off involved. Notably, the E-plane achieves 68% total efficiency at an f/D of 0.8, while the H-plane reaches 46% total efficiency at an f/D of 0.4. Striking a balance between utilizing the entire glass area and achieving desirable total efficiencies for both E-plane and H-plane, the optimal choice emerges as a square transmitarray design with an f/D of 0.6. This square design facilitates an effective compromise, ensuring efficient utilization of the glass area while achieving the desired total efficiencies in both planes.

Figure 2. Analysis of the focal length-to-diameter ratio on the (a) E-plane and (b) H-plane for the feeding quasi-Yagi antenna.

Unit cells

After evaluating the characteristics of the feed, the next design mission is the unit cells. This study employs eight distinct structures for the distribution of phase compensation. The discretization of phase compensation into eight unit cells necessitates each unit to possess a phase difference of 45°. For the design of the unit cells, the eight structures utilized must not only satisfy an integer multiple of 45° in phase differences among themselves but also consider the penetration loss incurred during transmission. Therefore, an analysis is conducted on the glass substrate to assess the structural implications of glass thickness, as illustrated in Fig. 3. The analysis reveals that at a glass thickness of 1.0 mm, the incurred penetration loss is approximately 2.6 dB. To enhance the phase tuning range of the designed unit cell, this study ultimately opts for a three-layer metal structure using two glass substrates with ε_r = 5.26 and a thickness of 0.5 mm. This choice aims to achieve a larger phase tuning range while considering the trade-off with penetration loss.

Figure 3. Penetration loss corresponding to different glass thicknesses.

The multilayer structure of the unit cell established from the above analysis is depicted in Fig. 4(a). This structure takes into account the fixed separation between the two glass substrates, namely, 0.01 mm. The next step involves analyzing the amplitude and phase shift variations caused by changing the geometric parameters of the unit cell. The objective is to identify structures that meet the criteria of penetration amplitude attenuation less than 3 dB and possess a phase tuning range of 315°. This analysis aims to explore how alterations in the geometric parameters of the unit cell impact the electromagnetic wave penetration structure.

Figure 4. (a) Side view, (b) 3D view, and top view of the unit cell (unit: mm).

Based on this profile, five unit cell topologies are developed, as shown in Fig. 4(b). The analysis of the amplitude attenuation and phase variation of the five unit cell structures concerning the length of the bar, denoted by L. The transmissive amplitude and phase are characterized and illustrated in Fig. 5.

Figure 5. (a) Magnitude and (b) phase of transmitting waves as the function of L.

For Configuration A, adjusting L can achieve a phase tuning range of 338°. However, Configuration A exhibits penetration losses greater than 3 dB when L ranges from 0.97 to 0.99 mm. This results in a significant reduction in the energy of the penetrating wave to half or even less. Additionally, at L ranging from 0.99 to 1.01, the phase sensitivity is excessively high. Choosing a structure with high phase sensitivity poses challenges in practical implementation, as it can lead to phase deviations due to fabrication errors, emphasizing the need for multiple structures in the design process.

Configuration B achieves a phase tuning range of approximately 205° when L ranges from 0.37 to 1.01 mm. Configuration C shows similar performance to Configuration B, featuring a hollow structure in the middle layer. By adjusting L, Configuration C achieves a phase tuning range of 209° when L ranges from 0.26 to 0.94 mm. Configuration D achieves phase tuning ranges of 101° (L: 0.20–0.66 mm) and 195° (L: 0.82–1.01 mm). Ensuring uniform phase differences among adjacent phase unit cells is crucial in the design of transmitarrays. Finally, Configuration E was developed with a phase tuning range of 95° (L: 0.24–0.66 mm) and 157° (L: 0.66–1.01 mm).

After analyzing unit cell structures for amplitude and phase shift variations using simulation software, eight unit cell structures were selected from the five types to compose the elements of the transmitarray. These structures were numbered based on their role as the phase reference point: Structure with a phase delay of 0° was assigned as Number 1, and structures with phase delays of 45°, 90°, and so forth, were consecutively numbered. The characteristics of unit cell are summarized in Table 1.

Table 1. Characteristics of the eight unit cells

It is worth noting that the proposed design method simplifies the optimization process by focusing on a single design factor (the length of the bar, L) and a single objective (phase). This streamlined approach allowed us to systematically tailor the unit cell structures to meet the performance requirements of the transmitarray, preventing the use of multiobjective optimization algorithms.

Transmitarrays

With these unit cells in hand, we can construct the unit cells based on the f/D identified by “Feed” and the phase distribution requirements for constructive interference. Specifically, when the feed source emits waves at an angle θ_i, and the coordinates of the ith unit element are (x_i, y_i), with (θ_b, φ_b) denoting the angle of transmitting beam focusing, k ₀ representing the propagation constant in free space, and d_i signifying the distance from the feed source to the ith unit element, the phase φ_T(x_i, y_i) on the ith unit element is determined by

(4)\begin{equation}\varphi \left( {{x_i},\,{y_i}} \right) = - {k_0}\left( {\sin {\theta _b}\cos {\varphi _b}{x_i} + \sin {\theta _b}\sin {\varphi _b}{y_i}} \right)\end{equation}

(5)\begin{equation}\varphi \left( {{x_i},{y_i}} \right) = - {k_0}{d_i} + {\varphi _T}\left( {{x_i},{y_i}} \right)\end{equation}

(6)\begin{equation}{\varphi _T}\left( {{x_i},{y_i}} \right) = {k_0}\left[ {{d_i} - \left( {{x_i}\cos {\varphi _b} + {y_i}\sin {\varphi _b}} \right)\sin {\theta _b}} \right]\\[4pt]\end{equation}

where φ(x_i, y_i) represents the phase shift introduced at the ith unit element, which is computed by the spatial coordinates of the unit element relative to the incident angle of the beam in equation (4). This equation illustrates how the phase shift at each unit element is influenced by its position within the transmitarray structure and the direction of the incident wave front. In equation (5), the term $ - {k_0}{d_i}$ accounts for the phase shift due to the propagation distance, while φ_T(x_i, y_i) represents the additional phase shift introduced by the unit element itself. This equation captures the combined effect of distance-related phase shifts and element-specific phase contributions, providing an understanding of the total phase shift experienced by each unit element. In equation (6), φ_T(x_i, y_i) represents the phase shift attributable solely to the unit element’s geometric configuration. The term ${d_i} - \left( {{x_i}\cos {\varphi _b} + {y_i}\sin {\varphi _b}} \right)\sin {\theta _b}$ accounts for the distance-dependent phase shift adjusted by the unit element’s spatial orientation relative to the incident beam angle (θ_b, φ_b). This equation elucidates how the geometric properties of each unit element modulate the phase of incident waves, thereby influencing the overall phase distribution across the transmitarray.

Given the goal of demonstrating the feasibility of the inkjet-printed transparent transmitarray in this paper, we designed three different sizes of transmitarray apertures, including 15 × 15 unit cells (3.5 λ × 3.5 λ), 20 × 20 unit cells (4.6 λ × 4.6 λ), and 25 × 25 unit cells (5.8 λ × 5.8 λ), where λ denotes the wavelength. According to the optimal f/D of 0.6, using the dimensions of these three transmitarrays, we can then determine the focal length (f). Specifically, the phase compensation distributions for the transmitarrays of 15 × 15, 20 × 20, and 25 × 25 unit cells are illustrated in Fig. 6. By assembling the eight numbered unit cells from “Transmitarrays” according to these phase compensation distributions, we obtain the transmitarray apertures, which are also shown in Fig. 6.

Figure 6. Aperture structure and 3D view of the (a) 15 × 15, (b) 20 × 20, (c) 25 × 25 transparent transmitarrays.

Results

For the 15 × 15 transmitarray, the reflection coefficients across the 27–29 GHz frequency range consistently fall below −10 dB, as shown in Fig. 8. Good impedance matching is achieved for the feed with transmitarray aperture considered. As for the radiation performance, Fig. 9 presents the radiation efficiency and realized gain, showing that measured results are slightly lower than the simulated ones. Figure 10 illustrates the simulated and measured patterns for the E-plane and H-plane at 28 GHz, showing an HPBW of 18.3° (E-plane) and 17.5° (H-plane) along with an FBR value of 12.01 dB. Overall, the measured broadside gain at 28 GHz is 14.87 dBi, indicating sufficient gain enhancement is achieved.

Figure 8. Simulated and measured reflection coefficient of the 15 × 15 inkjet-printed transparent transmitarray.

Figure 9. Simulated and measured (a) radiation efficiency and (b) realized broadside gain of the 15 × 15 inkjet-printed transparent transmitarray.

Figure 10. Simulated and measured (a) E-plane and (b) H-plane patterns of the 15 × 15 inkjet-printed transparent transmitarray.

Moving on to the 20 × 20 transmitarray, the reflection coefficients are depicted in Fig. 11, with a decreasing trend toward higher frequencies. At 28 GHz, the simulated and measured reflection coefficients are −16.9 dB and −25.8 dB, respectively. Figure 12 exhibits radiation efficiency and realized gain, where a measured gain of 16.94 dBi is attained. The measured efficiency is slightly lower than the simulated one. Figure 13 shows the simulated and measured two-dimensional (2D) patterns, with an HPBW of 13.1° (E-plane) and 12.4° (H-plane) along with an FBR value of 10.33 dB. The beam width is sharpened and varies as the aperture size.

Figure 11. Simulated and measured reflection coefficient of the 20 × 20 inkjet-printed transparent transmitarray.

Figure 12. Simulated and measured (a) radiation efficiency and (b) realized broadside gain of the 20 × 20 inkjet-printed transparent transmitarray.

Figure 13. Simulated and measured (a) E-plane and (b) H-plane patterns of the 20 × 20 inkjet-printed transparent transmitarray.

Extending the analysis to the 25 × 25 transmitarray, the reflection coefficients remain consistently below −10 dB within the 26–30 GHz range, as shown in Fig. 14. At 28 GHz, the simulated and measured reflection coefficients are −17.4 dB and −22.4 dB, respectively. The radiation efficiency and realized gain are provided in Fig. 15, and the simulated and measured 2D patterns at 28 GHz are depicted in Fig. 16. The broadside gain becomes 18.82 dBi, featuring an HPBW of 10.8° (E-plane) and 10.0° (H-plane) along with an FBR value of 19.10 dB.

Figure 14. Simulated and measured reflection coefficient of the 25 × 25 inkjet-printed transparent transmitarray.

Figure 15. Simulated and measured (a) radiation efficiency and (b) realized broadside gain of the 25 × 25 inkjet-printed transparent transmitarray.

Figure 16. Simulated and measured (a) E-plane and (b) H-plane patterns of the 25 × 25 inkjet-printed transparent transmitarray.

In summary, the measured performance of the inkjet-printed transmitarrays, including 15 × 15, 20 × 20, and 25 × 25 configurations, consistently demonstrates efficient operation with low reflection coefficients, high radiation efficiency, and desirable radiation patterns across the specified frequency ranges, confirming the effectiveness of the transparent inkjet-printed technology.

The performance of the proposed inkjet-printed transparent transmitarrays is compared with the state-of-the-art, as shown in Table 2. It illustrates the antenna performance comprising transparent transmitarrays or reflectarrays with different fabrication technology. These apertures exhibit various dimensions with different broadside gains. However, it is noteworthy that among the listed works, the current study stands out as the only one utilizing inkjet-printing technology to fabricate transparent transmitarray apertures. This pioneering approach offers several advantages, including enhanced flexibility, cost-effectiveness, and compatibility with transparent substrates, which are essential for inconspicuous deployments in urban architecture and integration with emerging technologies such as 5G millimeter-wave communication. The proposed structures, characterized by a frequency of 28.0 GHz, aperture dimensions from 3.5 × 3.5 λ ² to 5.8 × 5.8 λ ², and broadside gains from 14.9 to 18.8 dBi, demonstrate the efficacy of inkjet-printing with nanosilver particles in achieving high-gain performance for transparent transmitarrays. This comparative analysis underscores the novelty and significance of the current study in advancing transparent antenna technologies and highlights the potential for inkjet-printing to revolutionize the fabrication of high-performance antennas for various applications.

Table 2. Comparisons with transparent reflectarrays or transmitarrays designed at the millimeter-wave band

Comparison with copper microwires

Next, we present a comparison of the performance between inkjet-printed and copper microwire transmitarrays across varying sizes. The copper microwire counterparts were designed and fabricated through a conventional PCB process [Reference Chang, Lai and Chen16].

Beginning with broadside gain and gain enhancement, the inkjet-printed 15 × 15 transmitarray achieves a 14.87 dBi, with a gain enhancement of 7.29 dB. In comparison, the copper microwire counterpart records a gain of 15.11 dBi and a slightly higher gain enhancement of 7.53 dB. Examining the broadside gain for the inkjet-printed 20 × 20 transmitarray, we observe a gain of 16.94 dBi. In comparison, the copper microwire counterpart in the same size achieves a gain of 16.98 dBi. Scaling up to the 25 × 25 configuration, the inkjet-printed transmitarray demonstrates a gain of 18.82 dBi. On the other hand, the copper microwire counterpart at 25 × 25 showcases a gain of 19.55 dBi.

In terms of radiation efficiency, both inkjet-printed and copper microwire transmitarrays demonstrate high radiation efficiency, with values ranging from 78% to 84% and 80% to 83%, respectively. This suggests that inkjet-printing does not incur extra loss in the manufacturing process.

In summary, the comparative results indicate that the inkjet-printing technology achieves similar antenna gain and additional loss as compared to the PCB process. Also, our results persist as we scale to larger transmitarrays. This validates the inkjet-printing technology for transparent transmitarrays, enabling additional advantages including flexibility in design, compatibility with transparent substrates, and cost-effective, scalable manufacturing as compared to PCB. These factors contribute to the overall appeal of inkjet-printing technology in the development of transparent electromagnetic devices.

Potential applications

By integrating the proposed transmitarray structures into transparent surfaces, such as windows or glass partitions, within indoor environments, this technique enables the realization of a surfaces capable of manipulating incident electromagnetic waves to enhance signal reception and transmission for nearby base stations. These windows equipped with transparent transmitarrays function as passive beamforming elements, effectively focusing and steering radio frequency signals toward indoor base stations, thereby mitigating signal attenuation, multipath interference, and shadowing effects commonly encountered in indoor environments. By optimizing signal propagation paths and minimizing signal loss, our transparent transmitarray-enhanced windows contribute to significant improvements in signal quality, coverage, and data throughput for indoor base stations, ultimately enhancing the overall performance and reliability of indoor wireless communication networks.

Furthermore, the proposed transparent transmitarrays hold significant promise for applications in augmented reality (AR) and virtual reality (VR) systems. By seamlessly integrating transmitarray functionalities into transparent display panels, the proposed technique empowers AR/VR devices with enhanced imaging capabilities, beam steering, and immersive visual experiences. This integration paves the way for the development of lightweight, high-performance AR glasses and VR headsets, revolutionizing the way users interact with digital content and virtual environments.

Additionally, this study opens avenues for transformative applications in wireless communication networks and satellite communications. The deployment of transparent transmitarrays in satellite antennas enables efficient beamforming, signal focusing, and satellite tracking functionalities, thereby enhancing the performance and reliability of satellite communication systems. Moreover, in terrestrial wireless communication networks, transparent transmitarrays offer opportunities for dynamic beam steering, interference mitigation, and spectrum efficiency improvements, facilitating the deployment of next-generation 5G and beyond-5G networks.