High-Performance Radiation Design of a Planar Bow-tie Antenna Combined with a Dielectric Lens and Cascaded Matching Layers at Terahertz Frequencies

The demand for high-speed data transmission has increased significantly in the last decades. Terahertz (THz) frequency, which lies between 100 GHz to 10 THz, has been considered as the solution to the demand. However, the low gain and low efficiency of a THz antenna remain to be issues that hinder reasonable performance for various applications. This paper proposes the design of a high-gain and high-efficiency planar bow-tie antenna for applications in the THz frequency. A planar bow-tie on a high-resistivity silicon substrate is considered to obtain the broadband characteristics. To increase the gain and efficiency, a dielectric silicon lens and a matching layer based on the quarter-wavelength are applied in the design. From simulations using Computer Simulation Technology (CST) Microwave Studio, gain and radiation efficiency of up to 32.69 dB and 90.4% are obtained, respectively. This proposed design has shown high radiation performance suitable for high-speed transmission systems.

Bow-tie, High resistivity silicon lens, Matching layer, Terahertz

The terahertz (THz) wave radiation region, located between the microwave and the infrared regions, is the transition region between the electronic and photonic domains (Akyildiz et al., 2014). The THz wave is not applied as widely as the electronic and photonic domains, although there is potential for this frequency band. The availability of reasonable performance equipment, especially for THz wave sources and detectors, is one of the main issues of THz wave system development. As femtosecond lasers and photoconductive antennas have been available since the 1980s to produce THz waves (Mourou et al., 1981), some areas have begun to utilize these waves, such as medical science, pharmacology, and security (Siegel, 2002). This region has also been considered to fulfil the demand for high-speed wireless data transmission and various communication applications (Hirata et al., 2012). High-speed data transmission demand has increased significantly in the last decades. Some modifications have been made to improve data capacity by applying advanced modulation schemes and signal processing. In the future, a new spectral resource is needed to increase data speed. The large bandwidth of THz waves can be utilized to obtain higher data rates, even with the legacy data modulation technique. Therefore, a THz wave carrier frequency is necessary to increase bandwidth and fulfil requirements (Song & Nagatsuma, 2011).

2.1.   Planar Bow-tie Antenna

Figure 1 illustrates a schematic of the bow-tie antenna. It consists of two identical triangles separated by a specific gap distance. A discrete port with a 50 ? input impedance is used as the feeding method, set in the gap. High-resistivity silicon with a relative dielectric constant ( ) set to 11.9 was chosen due to its low refractive index dispersion and low absorption, which are suitable for electromagnetic wave radiations (Ronne et al., 1997). The thickness of the silicon wafer substrate of 300 µm is considered to comply with the availability of Si wafers on the market. The geometrical parameters of the antenna include antenna length (l), width (w), gap (g), flare angle (?), bar length (bl), and bar width (bw). The substrate dimensions consist of length (s) and thickness (h). As the bow-tie antenna performance can be treated as that of a dipole type antenna, 1 THz resonant frequency can be obtained by simply using half wavelength-dipole calculation or its periodic length pattern, such as ?/2, 3/2 ?, 5/2 ?, and so on (Wang & Zhan, 2013). The parameters of the antenna and the substrate are characterized to obtain a resonant frequency of 1 THz. Table 1 shows the optimum parameters after characterization for a resonant frequency of 1 THz. The length of the bow-tie antenna (l) is close to 3/2 ? of a 1 THz frequency. At a resonant frequency of 1 THz, the 300 ?m wavelength becomes shorter ( ). When the waves propagate in the silicon material (11.9), the wavelength is about 87 µm. As the planar antenna radiates most of its energy to the substrate side, it can lead to a surface wave problem on this side (Rebeiz, 1992). Therefore, the substrate dimension and thickness values are considered in order to deal with the substrate wave.

Figure 1 Schematic of the bow-tie antenna design on a high resistivity silicon substrate

Table 1 Antenna and substrate parameters

 2.2.    Silicon Dielectric Lens

An antenna placed on a thick dielectric substrate will radiate most of its energy into the dielectric side (Rebeiz, 1992). A hemispherical shape is used to minimize the internal reflection as well as the surface waves, so that radiation efficiency is increased. Figure 2 illustrates a dielectric lens designed on top of the substrate. To form a hemisphere shape, the lens radius (R) is set to 3000 µm, or half the dimension of the Si substrate (s). The center point of the lens is at the top of the substrate, or at the point of substrate thickness (h). The lens dielectric constant is determined to be same as the substrate dielectric constant to avoid a mismatched condition between the two.

Figure 2 Schematic of a dielectric lens structure

3.1.    Planar Bow-tie Antenna

This section discusses the simulation results of the planar bow-tie antenna shown in Figure 2. The discussion is conducted for two parameters, i.e. return loss and radiation pattern.

3.1.1.   Return loss (S11) parameter

Figure 3 shows the S11 simulation results of the bow-tie antenna. The line is not smooth, which indicates internal reflections occurring in the substrate. This issue can be solved by adding a hemispherical lens to provide a radiation vector parallel to the hemispherical surface vector. The return loss at 1 THz is around -20 dB. The bandwidth, which is determined at the threshold of -10 dB, is 364.97 GHz. Therefore, the result shows that the antenna’s resonant frequency is 1 THz and has broad bandwidth characteristics, as expected from a conventional bow-tie antenna design.

Figure 3 S11 parameter simulation results of the initial bow-tie antenna design

3.1.2.   Radiation pattern

Figure 4 shows the radiation pattern simulation results at 1 THz frequency for planes of (a) ? = 0° (E-plane) and (b) ? = 90° (H-plane), respectively. The red and green lines represent the gain levels for all directions and the side lobe level, respectively. Both figures show that the radiation patterns are not as desired. This issue is related to the internal reflections, which lead to the radiated power being trapped in the substrate or surface waves. The problem can be solved by considering infinite substrate thickness or by providing a substrate surface with normal vectors to all radiation vectors. We consider the latter solution to solve this issue. The realized gain is -4.631 dB. The radiation efficiency and total efficiency are -13.97 dB (4%) and -14.01 dB (3.9%), respectively. The radiation pattern seems to be omnidirectional. The main lobe is directed at -53° (E-plane) and 56° (H-plane), which means that the antenna cannot radiate the energy directly to the desired direction (0^o) from its center point. Although the angular beam width is narrow at the main lobe, these results indicate that the antenna is not applicable for implementation in practical use, because most of the power radiated from it is reflected back into the substrate, while the radiated power to free space is very low.

Figure 4 Radiation patterns of the bow-tie antenna for: (a) ? = 0°; and (b) ? = 90°

3.2.    Bow-tie Antenna Combined with a Dielectric Lens

This section discusses the simulation results of the bow-tie antenna combined with a dielectric lens, as shown in Figure 2. The discussion relates to two parameters, return loss and radiation pattern.

3.2.1.   Return loss (S11) parameter

Figure 5 shows the S11 simulation results of the bow-tie antenna combined with a silicon dielectric lens. The resonant frequency of 1 THz remains at around -20 dB, while the bandwidth determined at the threshold of -10 dB is 368.76 GHz. The S11 parameter shows that the antenna is still able to resonate at 1 THz and has broadband characteristics. These results indicate that the addition of the dielectric lens changes neither resonance nor bandwidth. The return loss line in Figure 5 is smoother than that in Figure 4, implying that the surface waves have been successfully minimized by the combination of the bow-tie antenna with the dielectric lens. The plot of gain for some frequencies shows that the gain fluctuates around 10 dB, and the highest gain is not at the resonant frequency of 1 THz. We expect the highest gain to be at the resonant frequency. Therefore, this structure is not yet at the optimum condition. In subsection 3.3 we investigate the optimum gain by characterizing substrate thickness. This technique is intended to find a focal position to produce higher directivity.

Figure 5 S11 Parameter simulations of the bow-tie antenna combined with dielectric lens

3.2.2.   Radiation pattern

Figure 6 shows the radiation pattern simulation results of the bow-tie antenna combined with a dielectric lens at 1 THz for a plane of (a) ? =  (E-plane) and (b) ? =  (H-plane). The highest realized gain is 10.18 dB, obtained from the main lobe magnitude of Figure 6a. The radiation and total efficiency are -1.592 dB (69.3%) and -1.63 dB (68.7%), respectively. The realized gain and efficiencies were obtained from the 3D farfield simulation results at the frequency of 1 THz. The results indicate that the dielectric lens has increased the efficiency and gain performance of the antenna; nevertheless, the main lobe direction and angular width are not suitable for the antenna to radiate its power with high directivity in a desired direction. Therefore, an optimization process is necessary to improve the results. In the following steps, substrate thickness characterization and multilayer antireflection coating were applied to improve the results. 

Figure 6 Radiation pattern of the bow-tie antenna combined with dielectric lens at: (a) ? =  (E-plane); and (b) ? =  (H-plane)

3.3.    Substrate Thickness Characterization

In this stage, optimization is conducted to further improve the directivity by varying the substrate thickness. The antenna and dielectric lens geometry are kept constant, as detailed in Table 1, and the iteration in thickness is conducted from 300 µm to 1100 µm. The effect of thickness will be discussed in terms of gain, efficiency and angular beam width.

3.3.1.   Gain

Figure 7 shows the gain for different substrate thicknesses. The gain increases for thicknesses of 300 µm to 1000 µm and subsequently decreases. The maximum gain of 31.31 dB is obtained at a thickness of 1000 µm and produces a significant gain improvement until 20 dB compared to the initial thickness. High gain is necessary to mitigate the high attenuation when the radiation propagates in the atmospheric free space. The results show that the substrate thickness affects the antenna’s directivity, and the optimum gain can be obtained at a certain thickness.

Figure 7 Gain versus substrate thickness

3.3.2.   Radiation efficiency

Figure 8 shows the radiation efficiency for different substrate thicknesses; a maximum efficiency of 71.8% is obtained at the substrate thickness of 900 µm, but efficiency starts to drop from a thickness of 1000 µm and beyond. From the results, we can conclude that substrate thickness has a slight effect on the antenna’s efficiency. This condition comes from the radiation wavefront conforming with the lens surface, where the optimum thickness to pass through the interface is around 900 µm.

Figure 8 Radiation efficiency versus substrate thickness

3.3.3.   Angular beamwidth

Figure 9 shows the beam width at plane ? =  versus the substrate thickness. The smallest beam width is , obtained at a thickness of 1000 µm. The results indicate that the substrate thickness causes the radiation pattern to be more directive when the beam width becomes narrower. The narrow beam width pattern is useful in providing high-resolution imaging when the antenna is used in THz imaging applications. 

Figure 9 Beamwidth versus substrate thickness

3.4.    Antireflection coating implementation

A common problem with lens antennas is that the incident wave is partially reflected back to the substrate at the lens-air interface, thereby affecting radiation efficiency (van der Vorst et al., 1999). Studies on canceling internal reflection in a dielectric lens have been performed since 1954 using quarter-wave antireflection coating (Morita & Cohn, 1956). The coating works according to the principle of phase changing between the reflected waves and depends on the different refractive indices of the lens and the coating. The phase changing results from ray propagation through the coating, and because of the different path lengths between subsequent rays which leave the substrate at different points, based on a far-field observation point. The coating is theoretically designed using an infinite number of internal reflections. The derivation of the infinite reflection and transmission coefficients use the model and configuration described by van Houten & Herben (1994). In this section, an antireflection coating, otherwise known as a matching layer (ML), is designed using different techniques.

3.4.1.   Quarter-wave matching layer

Figure 10 shows the proposed ML structure. The dielectric constant ( ), effective wavelength ( ) and thickness (d) of the quarter-wave ML are obtained by Equations 1, 2 and 3, respectively.  is the dielectric constant of air, which is one. is the wavelength in free space for the 1 THz frequency, and  is the effective wavelength of the ML. By using 11.9 as the silicon dielectric constant ( ), the effective dielectric constant and the layer thickness (d) are 3.45 and 40.4 µm, respectively, as calculated by Equations 1 to 3 (van der Vorst et al., 1999). The geometry of the antenna and dielectric lens are kept constant, as mentioned in section 2. The substrate thickness (h) is 1000 µm and is obtained from the thickness of the optimum gain and beam width in section 3.

Figure 10 Schematic of the matching layer design

From the design shown in Figure 10, the radiation efficiency and gain have increased to 83.1% and 32.31 dB respectively. It is clear that the matching layer has lowered the internal reflection significantly, but not completely. The efficiency improvement is not as good as that reported by van der Vorst et al. (1999), because the antenna already has a narrow beam width and good directivity. In addition, the proposed lens antenna has different angles of incident at every different surface position. Therefore, the single quarter-wavelength matching layer does not completely reduce the reflection effect on the lens antenna, because it can only reduce the internal reflection if the wave vector is parallel to the normal vector. An optimum matching layer with non-uniform thickness is more preferable, but we do not study this because it is difficult to design and not practical in real conditions. We consider a cascaded matching layer, which will be discussed in the following section.

3.4.2.   Cascaded matching layer

The concept of the cascaded matching layer is the same as that of the quarter-wave in the previous subsection, but with multiple-layer implementation. The dielectric constant and thickness of each layer can still be obtained using Equations 1 to 3, derived into Equation 4.

                                       (4)

 is the dielectric constant of every layer in an n-ML design and  is the dielectric constant of the substrate material. The effective wavelength and thickness of every layer can be obtained using the dielectric constant obtained from Equation 4. Theoretically, a higher number of matching layers corresponds to better performance in terms of radiation characteristics such as gain and efficiency (Tokan, 2014). In this paper, the effects of 15 matching layers are studied, to find an ideal number based on their performance. A sample schematic of a ten-layer design of the cascaded matching layer is shown in Figure 11, which depicts the layers stacked on top of the dielectric lens. To avoid overlapping layers, an insertion technique is applied in CST. The thickness of each layer obtained from Equation 4 is distinct, where the higher-level layer is thicker. Other dimensions of the design are kept constant, as in the previous design. The complete list of dielectric constants of the cascaded MLs from one ML to 15 MLs is summarized in Table 2.

As shown in Figure 12, the radiation efficiency shows incremental values from one ML to 15 MLs, with a maximum value of 93.7% at 15 layers. The results show that a higher number of MLs can reduce more internal reflection, thus increasing the radiation efficiency. The gain value also shows incremental values from one ML to four