1. Introduction

Optical antennas, counterparts of the microwave and radiowave antennas, have become vital components of wave optics, empowering the manipulation and control of light at nanoscale [1,2]. These devices can couple localized energy to freely propagating optical radiation and vice versa [3]. In particular, the directional optical antennas have shown the ability to guide light efficiently in desired directions [4], thus making them suitable for a range of exciting applications, such as integrated optical devices, low-loss photonic circuits, ultrasensitive sensors, and optical neural networks [5]. Using plasmonic materials for such structures comes with the benefits of having a resonant nature and a smaller footprint [6–9], which are widely utilized for different features like color routing [10,11], directional Raman scattering [12,13], cathodoluminescence emission [14,15], etc. However, metals exhibit large ohmic losses, which makes their alternative, dielectrics, more attractive owing to their low losses and broadband nature [16–23]. This niche has been enriched with a variety of geometry configurations made of materials with moderate or high refractive indices, like titanium dioxide [24], silicon [25], germanium [26], gallium arsenide [27], etc. Plenty ideas for designing these optical nanoantennas find their origin coming from the traditional macroscopic designs. One such pioneering example is the Yagi-Uda antenna, typically consisting of a reflector, a feed element and two or more directors. Besides, many hybrid metal-dielectric antennas have also been studied which inherit the advantages of both, plasmonic and dielectric antennas [28,29].

Optical traveling wave antennas, which utilize the propagation of waveguide modes as the mechanism of radiation along the non-resonant guiding structure, have been used to target highly directional patterns [30,31]. In particular, a subset of these antennas, leaky-wave antennas, have already shown to exhibit good directionality through the leakage originating from their leaky-modes [32–37]. Moreover, traveling wave antennas which support guided modes in addition to leaky modes have shown excellent directional characteristics [38–41]. Furthermore, these antennas also exhibit a broad bandwidth, high front-to-back ratio, and small side lobe level, making them robust examples for inter-chip communication [42].

The directional characteristics of optical antennas depend on the geometry, material constituting the antennas, footprint of the structure, and frequency of operation. For achieving an optimal performance of such antennas, one requires a meticulous designing and optimization strategy. Depending on the optimization problem at hand, the number of parameters affecting it, and the size of the parameter space for finding a solution, plenty optimization schemes including particle swarm, genetic, and evolutionary algorithms, have been extensively employed [43–45]. Although these traditional optimization methods have proven to be robust and efficient, they can be time consuming for complex optimization problems with many degrees of freedom. In this context, the inverse design method in conjunction with deep-learning neural networks has recently shown to successfully explore a full-space of possible designs and furnish non-intuitive results [46–49]. These techniques could also give rise to a new class of directional antennas.

In this article, we present a comprehensive numerical and experimental analysis of traveling-wave antennas made of tantalum pentoxide (Ta$_2$O$_5$), furnishing a highly directive emission. Our dielectric antennas consist of two elements, namely, the reflector and director, positioned over a glass substrate. Specifically, three different types of directors comprising the rectangular-, horn-, and tip-shaped geometries were designed. We utilize full-wave numerical simulations, which employ the particle swarm optimization (PSO) in conjunction with the trust-region method (TRM) to achieve robust antennas with high directive gains. Our results reveal that the directivity and main lobe emission are majorly governed by two guided transverse electric modes that radiate from the end facet of the director. Additionally, the experimentally produced optimized structures, fabricated using a two-step electron-beam lithography, demonstrate highly directional characteristic in the far field emission patterns and are in a good agreement with the numerical results. Furthermore, our optimized antennas exhibit a broadband nature making them robust to fabrication imperfections. We anticipate that the non-resonant, broadband nature of our optical antennas can be practically utilized in realizing new applications for sensing and optical communication.

2. Numerical and experimental methods

Here, we provide details of our numerical and experimental setup for the characterization of the guided wave antennas investigated in this work. We study three different antennas made of Ta$_2$O$_5$, each comprising of a rectangular reflector and a rectangular-, horn- or tip-shaped director, as illustrated in setups shown in Fig. 1(a), Fig. 2(a) and Fig. 3(a), respectively. The antennas with a refractive index of $n=2.0978+0.0012487i$ are deposited on a SiO$_2$ substrate with a refractive index of $n_g=1.52$ [50]. The intermediate refractive index with low losses in combination with the fact that Ta$_2$O$_5$ can be easily evaporated, makes this material a suitable candidate for our studies. A dipole emitter with an emission wavelength of $780$ nm and a dipole moment along the $y$-axis is used as the source of excitation having a power of 1W. It is placed between the reflector and the director at the origin of $y$-axis, $10$ nm above the substrate mimicking a finite emitter size. This is represented with a red spot in all the numerical setups. Considering the random orientations of the quantum dots, it has already been demonstrated in our previous work that this position and orientation of the emitter produces the strongest coupling to the antenna, while the $x$- and $z$-oriented dipoles produce considerably weaker signals [38].

All antennas are oriented along the $xy$-plane and have the direction of wave propagation along positive $x$-axis. The finite integration technique (FIT) in time-domain is used for the numerical calculations of electromagnetic fields [51]. The simulation models employ a multi-layer environment with air above and SiO$_2$ below the antenna. An open-boundary condition is applied to represent a perfectly matched layer (PML) around the computational domain. The directive gain is calculated in the far field at a sufficiently larger distance from the antenna. The optimization is performed using a combination of global and local optimization techniques, namely, the particle-swarm and trust-region algorithm. They optimize the maximum directive gain (directivity) defined as ratio of the peak intensity to the intensity averaged over all directions. Further details on the numerical setup are given in our previous work [42].

For the experiment, the optimized samples are fabricated by using a two-step electron-beam lithography process. We use a standard microscope coverslip as the substrate and spin coat a $220$ nm thin layer of the positive tone resist poly(methylmethacrylate) (PMMA). Conductivity is provided by another thin, spin coated layer of Electra 92 (Allresist) placed on top of the PMMA film, which can be easily dissolved in distilled water. In the first lithography step, the geometry of the antennas are patterned by the electron beam. Subsequently, we develop the sample and remove the exposed PMMA with an appropriate developer. Then, a thin film of Ta$_2$O$_5$ (layer thickness of $100$ nm or $210$ nm, depending on antenna design) is deposited via electron-beam evaporation. After evaporation, we put the sample in a bath of N-Methyl-2-pyrrolidone (NMP) annealed at 60 $^\circ$C for 2.5 hours and remove the remaining PMMA. In the second lithography step, we define a small area of $200$ nm$\times 200$ nm in the feed gap between director and reflector, in which several hundreds of colloidal quantum dots (QDs) made of CdSeTe with a ZnS shell (Qdot 800 Carboxyl Quantum Dots, Thermo Fisher Scientific) are deposited, following the PMMA mask development. These QDs possess a central emission wavelength of $780$ nm and are used as the internal light sources. To guarantee that the QDs stick to the substrate, a chemical linking procedure is performed which facilitates the formation of covalent bonds between the colloidal QDs and the substrate. A detailed description of the chemical linking process can be found in Ref. [32]. A final lift-off process in NMP removes the remaining PMMA.

The far field emission patterns of the antennas driven by the QDs are analyzed by Fourier imaging, and the emission angle of the light is retrieved from the Fourier plane of the objective. The QDs are excited with a blue pump laser (wavelength $\lambda =453$ nm) through the glass substrate via a high resolution oil objective (100x magnification, numerical aperture $NA=1.49$) and the subsequent emission is then collected by the same objective. A combination of dichroic beamsplitter and longpass filter are introduced in order to filter out the pump light. The back focal plane of the objective is then imaged onto an electron multiplying charge-coupled device (EMCCD) camera. For a schematic illustration of the experimental measurement setup, see Ref. [38]. Finally, the measured far field emission patterns are normalized to the maximum directive gain of the corresponding numerical results.

3. Results and discussion

3.1 Optimization of Ta$_2$O$_5$ rectangular antennas

We start our study with the optimization of an antenna composed of a rectangular director and reflector as shown in Fig. 1(a). Seven geometrical parameters are used for optimizing the antenna structure, targeting its highest directivity (cost function). These parameters are the reflector length ($RL$) and width ($RW$), director length ($DL$) and width ($DW$), distance of the field source from the director ($DD$) and reflector ($RD$), and height of the antenna structure ($H$). The optimal values for these parameters obtained from the optimization process using the particle swarm algorithm in conjunction with the trust-region method are presented in Fig. 1(g). The near-field of the optimized antenna shows that the directive nature of the antenna stems from the propagation of three guided TE modes in addition to the leaky modes excited by the dipole emitter (see Fig. 1(b)). Our analysis demonstrates that most of the optical power is coupled to the TE$_{0,0}$ and TE$_{0,2}$ modes. Their mode profiles and the amount of power coupled to them are highlighted in Fig. 1(c), showing their key importance in governing the directive emission characteristics. Figure 1(e) presents the calculated linear directive gain with tightly focused main lobe emission pointing at a polar angle of $\theta =69^\circ$ and azimuthal angle $\varphi =0^{\circ }$. A high directivity of $63.1$ ($18$ dB) is achieved due to the interference exhibited by the excited modes, predominantly originating from the end facet. To validate our results, we fabricated our optimized antenna, whose scanning electron micrograph is depicted in Fig. 1(d). The red box in the image indicates the area of quantum dot deposition. The measured far field intensity distribution in Fig. 1(f) is in good qualitative agreement with the numerical calculations, though some discrepancies in higher polar angles are observed. This is because the numerical aperture used in the experiments limits the highest collection angle to $\theta _{NA}=79^{\circ }$. The slight shift of the main lobe from the antenna axis ($\varphi =0$) is attributed to the displacement of the quantum dots cloud from the optimal, central position along the $y$-axis [38]. Finally, the ring-like feature around $\theta =41^{\circ }$ stems from uncoupled QDs emitting directly into the substrate in all azimuthal angles.

 

Fig. 1. Ta$_2$O$_5$ rectangular antenna. (a) Schematic representation. The antenna is composed of the Ta$_2$O$_5$ reflector and rectangular director on a SiO$_2$ substrate, defined by seven design parameters affecting the directivity: the antenna height ($H$), director length ($DL$) and width ($DW$), reflector length ($RL$) and width ($RW$), distance of the field source from the director ($DD$) and the reflector ($RD$). The antenna is excited by a dipole source emitting at $780$ nm (red spot). (b) The calculated electric near-fields $|E|$ (linear scale) of the optimized antenna in the $xy$-plane at $z=50$ nm. (c) Calculated electric field intensity distribution of the first three guided modes excited by dipole emitter in the director together with the amount of power coupled to them. (d) Scanning electron micrograph of the antenna design with the red square marking the region of deposited QDs. (e) Calculated angular linear directive gain distributions of the antenna exhibiting an in-plane directivity of $D=63.1$ at $\theta =69^{\circ }$. (f) Measured far field intensity normalized to theoretical maximum. (g) Design parameters obtained from the optimization process.

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3.2 Optimization of Ta$_2$O$_5$ horn antennas

It has been recently demonstrated that horn-shaped antennas made of HfO$_2$ and Si are capable of furnishing high directivity in a broad frequency range [42]. Therefore, we optimize here a Ta$_2$O$_5$ horn-shaped antenna aiming to retain similar attractive functionalities but with an advantage of more simplicity in the evaporation process compared to some other materials. The numerical setup together with the nine geometrical parameters used in the optimization and their optimal values are illustrated in Fig. 2(a) and Fig. 2(g), respectively. The electric near-field distribution of the optimized antenna (Fig. 2(b)) clearly shows the interference of different modes excited in the director. This color map displays also the radial-like patterns emerging from the horn section with negligible back reflection. Actually, our mode analysis unveils four TE and three TM modes supported in the rectangular section of the director with most of the optical power being coupled again to the TE$_{0,0}$ ($26$%) and TE$_{0,2}$ (19%) modes. Additionally, other higher order modes are weakly excited in the horn-section of the director. The resultant directive gain distribution of such an antenna, as depicted in Fig. 2(e), exhibits an enhanced linear directivity of $119$ ($20.75$ dB) in comparison to its rectangular-shaped counterpart. The main radiation lobe with a needle-like shape points at $\theta =41^{\circ }$ and $\varphi =0^{\circ }$ direction. Besides, the far field pattern also reveals the increased side lobe level expressed in the form of a chain of many highly focused spots along $\varphi =0^{\circ }$. Interestingly, our optimized Ta$_2$O$_5$ horn-shaped antenna possesses quantitatively similar far field emission features for the directivity, main lobe angle, and side lobe level as its HfO$_2$ sibling theoretically studied in Ref. [42]. Furthermore, it has almost the same flare angle for the horn section of the antenna, i.e., $\approx 12^{\circ }$. A scanning electron micrograph of the fabricated optimized horn-shaped antenna and its experimentally measured far field intensity distribution are shown in Fig. 2(d) and (f), respectively. In general, the experimental far field is in good agreement with its numerical counterpart (Fig. 2(e)), especially for the position of the main lobe radiation. However, the main lobe and side lobes are not as clearly separated in polar direction in the experimental data as in the calculations. This fact can most likely be attributed to the distribution of QDs around the ideal position, which leads to a broadening of the resulting emission pattern. Since the expected side lobes are quite small, this effect is more noticeable here compared to the rectangular shaped antenna discussed before. Moreover, the distribution of emission wavelengths of the QDs as well as the final angular resolution of the optical setup could play a role.

 

Fig. 2. Ta$_2$O$_5$ horn antenna. (a) Schematic representation. The antenna is composed of the Ta$_2$O$_5$ reflector and horn-shaped director on a SiO$_2$ substrate, defined by nine design parameters affecting the directivity: the antenna height ($H$), director length ($DL$) and width ($DW$), horn length ($HL$), horn width at the radiating end ($HW$), reflector length ($RL$) and width ($RW$), distance of the field source from the director ($DD$) and the reflector ($RD$). The antenna is excited by a dipole source emitting at $780$ nm (red spot). (b) The calculated electric near-fields $|E|$ (linear scale) of the optimized antenna in the $xy$-plane at $z=105$ nm. (c) Calculated electric field intensity distribution of the first seven guided modes excited by dipole emitter in the rectangular section of the director together with the amount of power coupled to them. (d) Scanning electron micrograph of the antenna design with the red square marking the region of deposited QDs. (e) Calculated angular linear directive gain distributions of the antenna exhibiting an in-plane directivity of $D=119$ at $\theta =41^{\circ }$. (f) Measured far field intensity normalized to theoretical maximum. (g) Design parameters obtained from the optimization process.

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3.3 Optimization of Ta$_2$O$_5$ tip antennas

Aiming to further improve the directivity and being inspired by the classical Yagi-Uda antenna consisting of a reflector and several directors, we studied the effect of changing the radiating end of the already optimized rectangular-shaped antenna in Fig. 1, by introducing some additional directors to it. In the typical Yagi-Uda antennas, adding more directors results in increased in-plane directivity, but after a certain number of added directors, the effect of adding new directors becomes negligible, as it only results in very small improvement in the directivity but at the cost of increased footprint of the structure. In the new design, we add five identical director elements to the optimized rectangular shaped antenna. For the optimization, we introduce three new parameters, namely, the additional director length ($ADL$) and width ($ADW$), as well as the spacing between the elements ($S$). The height of the additional directors is kept identical to the fundamental structure for the sake of simplicity in fabrication. Interestingly, the resulting optimized structure has all its additional directors merged without gap, i.e. $S=0$, into a single tip-like element with a length of $ADL=4200$ nm and width of $ADW=400$ nm connected to the main director, as illustrated in Fig. 3(a).

 

Fig. 3. Ta$_2$O$_5$ tip antenna. (a) Schematic representation. The antenna is composed of a Ta$_2$O$_5$ reflector and director with tip-shaped extension on a SiO$_2$ substrate, defined by the following design parameters affecting the directivity: the antenna height ($H$), director length ($DL$) and width ($DW$), additional tip-like director length ($ADL$) and width ($ADW$), reflector length ($RL$) and width ($RW$), distance of the field source from the director ($DD$) and the reflector ($RD$). The antenna is excited by a dipole source emitting at $780$ nm (red spot). (b) The calculated electric near-fields $|E|$ (linear scale) of the optimized antenna in the $xy$-plane at $z=50$ nm. (c) Calculated electric field intensity distribution of the first three guided modes excited by dipole emitter in the director together with the amount of power coupled to them. (d) Scanning electron micrograph of the antenna design with the red square marking the region of deposited QDs. (e) Calculated angular linear directive gain distributions of the antenna exhibiting an in-plane directivity of $D=96.5$ at $\theta =70^{\circ }$. (f) Measured far field intensity normalized to theoretical maximum. (g) Design parameters obtained from the optimization process.

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The radiation characteristics of the antenna can be understood from the simulated electric near-field pattern (Fig. 3(b)) and profiles of the excited modes (Fig. 3(c)). Actually, the dipole emitter effectively couples to two dominant TE$_{0,0}$ and TE$_{0,2}$ modes in the fundamental section of the antenna, having approximately $20\%$ and $16\%$ of the total optical power transferred to them, respectively. However, the cross-section of the additional element of the antenna supports no new guided modes but only leaky modes, which becomes evident from the vanishing guided propagation along the tip of the antenna (Fig. 3(b)). Therefore, the increased directivity of the tip antenna comes from an interplay between the guided and leaky modes. Far field emission pattern demonstrated in Fig. 3(e) exhibits a remarkable improvement in the linear directivity of up to $96.5$ ($19.85$ dB) and a reduced side lobe level of the radiation pattern as compared to the simple rectangular-shaped antenna, while radiating at almost the same main lobe angle $\theta =70^{\circ }$. The scanning electron micrograph of the fabricated antenna and its experimentally measured emission pattern are presented in Fig. 3(d) and (f), respectively. Good agreement between simulated and measured far field patterns with respect to directionality and side lobe level is observed. Incidentally, the difference in the azimuthal angle of the main lobe is attributed to the displacement of the QDs, same as in the case of rectangular-shaped antenna. Finally, we would like to note here that the directivity of the tip antenna can be further increased to the magnitude of the horn antenna by adding two additional tip elements at the end of the main rectangular section, at the positions where other two hot spots in the near-field plot of Fig. 3(b) are located, i.e., at both sides from the central hot spot. Our calculations (not present here) show that such fork-like structure, in which three tips serve as channels for the guided propagation, exhibits an even further increased linear directivity of 110.

The discussion above has revealed the drastic influence of the additional tip element on the overall emission properties of the antenna. Therefore, in the following, we further explore how dimensions of the additional element impact the far field radiation pattern. Figure 4 illustrates the directivity (blue curves) and angle of the main lobe (gray curves) of the antenna as a function of its tip length, width, and height of the whole structure. The red circle in each plot represents the chosen optimized value for that respective parameter. Interestingly, all three parameters significantly affect the directivity, but not all influence the main lobe angle. The directivity smoothly converges to the optimal value as a function of tip length (Fig. 4(a)), while it shows a resonant behavior as a function of tip width and antenna height, associated with different modes excited within such director cross-sections, as seen in Fig. 4(b) and (c). Unlike the directivity, the main lobe angle of emission is not affected by the tip length and width but it is dynamically governed by the antenna height only. This is attributed to the smooth transition from the leaky-wave structure for the small height to guided-wave structure with the continuously increasing number of higher-order guided modes excited inside the director as the antenna height increases. Ultimately, these plots nicely demonstrate the possibility to tailor the directivity and main lobe angle over wide ranges by changing the tip dimensions and height of the antenna structure, respectively.

 

Fig. 4. Dependence of the directivity of the optimized Ta$_2$O$_5$ tip antenna shown in Fig. 3 on the design parameters: (a) the additional director length and (b) width, and (c) antenna height. The red circle and dashed line on each plot represent the chosen optimal value of the corresponding parameter, as shown in the tables of Fig. 1(g) and Fig. 3(g) that results in the linear directivity of $96.5$. The gray curve in each plot shows evolution of the main lobe polar angle $\theta$ for the corresponding design parameter.

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4. Comparison of all antennas

To facilitate the comparison of the three antennas introduced in this work, we summarize their radiation characteristics in this section. In Fig. 5(a), we plot the directive gain of each antenna in the forward direction of propagation as a function of polar angle $\theta$ at $\varphi =0^{\circ }$ along with the gain without presence of any antenna (gray curve). The rectangular- and tip-shaped antennas have their main lobes pointing almost in the same direction, i.e., $\theta =69^{\circ }$ and $70^{\circ }$, respectively. This is reasonable as both the antennas have the same height ($100$ nm) which is one of the most influential parameter governing the main lobe angle, as elucidated in our Fig. 4(c) (gray curve) and previous work [42]. In contrast, the horn antenna has the main lobe emission directed at completely different angle of $\theta =41^{\circ }$, attributed to its significantly different height ($210$ nm). Note that all antennas demonstrate an in-plane directivity, which is evident from the inset showing all main lobes aligned at $\varphi =0^{\circ }$ for their respective polar angles $\theta$. Besides, while the rectangular- and tip-shaped antennas exhibit a near-unity radiation efficiency, the horn antenna has an efficiency of $90\%$ due to the increased volume (height, width) of the slightly absorbing antenna material. Figure 5(b) additionally compares the forward directivity (at $\varphi =0^{\circ }$) of the antennas as a function of the operational frequency. Essentially, all our antennas exhibit the broadband nature, maintaining a directivity of above $50$ in the wide frequency range from $\sim 350$ to $\sim 430$ THz. We also validate this nature by analyzing the electric near-field distributions of these antennas for different frequencies in the range of $300$-$580$ THz, which show a non-resonant behavior with their continuously increasing electric field amplitudes as a function of the operational frequency (see Fig. S1 in Supplement 1). Interestingly, the tip antenna exhibits a much broader bandwidth in comparison to the other two antennas, though, one might intuitively expect a better performance from the horn antenna. Finally, Fig. 5(c) gives a summary of the radiation characteristics of the investigated antennas including the directivity, front-to-back ratio (F/B), main lobe angle, angular width of the main lobe, and side lobe level [42]. In particular, the tip antenna demonstrates the highest front-to-back ratio and the lowest side lobe level, which in addition to its broad bandwidth and high directive nature makes it a robust candidate for a wide range of applications. Overall, we could summarize the design rule for such antennas under three aspects, namely, the in-coupling (efficient coupling to the dominant TE modes), propagation (beating of modes) and out-coupling of the radiation (impedance matching). This can be achieved by adjusting the antenna’s geometrical parameters and, therefore, could be used as a general guide in the design of high directive antennas of different dielectric materials in the optical regime. Finally, we provide a small survey highlighting the performance of our antennas with respect to other plasmonic [52,53], dielectric [19,32,54] and hybrid antennas [29] (see Table 1).

 

Fig. 5. Comparison of the three investigated antennas in this work. (a) Calculated directive gain of the rectangular- (blue curve), horn- (red curve), and tip-shaped (green curve) antennas as a function of polar angle $\theta$ at $\varphi =0^\circ$, highlighting the directions of the main lobe emission (black dashed lines). The inset shows the directive gain of the antennas as a function of azimuthal angle $\varphi$ at the directions of the respective main lobe emission angle $\theta$. (b) Forward directivity of the corresponding antennas as a function of the operational frequency, showing their broadband nature. The black dashed line indicates the frequency used in our study. (c) The table summarizes the radiation characteristics such as directivity, front-to-back ratio (F/B), main lobe angle, angular width at $-3$ dB, and side lobe level of the proposed antennas.

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Table 1. Comparison of characteristics of different antennas with respect to their design, material, operational wavelength, directivity and approximate bandwidth.

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5. Conclusion

We optimized three types of traveling-wave antennas composed of Ta$_2$O$_5$. The results demonstrate the highly directive characteristics of our antennas with linear directivities as high as 63, 97 and 119 for the rectangular-, tip-, and horn-antenna, respectively. This directionality originates mainly from two dominant TE modes in conjunction with the leaky modes. These antennas are not just ultra directive, but they also showcase high efficiency and a wide operating frequency range while being robust with respect to fabrication tolerances, especially, the tip antenna. Furthermore, they offer an opportunity to tailor the directivity and main lobe angle. Our numerical simulations have been validated by good agreement with the experimental results obtained from the fabricated samples. Despite the larger footprint, the feasibility of sample production shows that these antennas can be efficiently used in suitable practical applications like integrated optical devices, on-chip communication, beam shaping, and wireless communication. Finally, the direction properties of such antennas can be further enhanced by utilizing them in an array design.