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Abstract
In this paper, for the first time, the idea of a dielectric director has been utilized to improve the directivity and gain of the proposed hybrid plasmonic rhombic nano-antenna (HPRNA). The proposed HPRNA can support a horizontal radiation pattern to flourish the concept of wireless transmission link. The horizontal radiation pattern has a 3 dB beamwidth of 43.5°, side lobe level of −11.9 dB, and a directivity and gain of 10.5 dBi and 10.3 dB, respectively, at the operating frequency of 193.5 THz. Moreover, the effects of geometric parameters to verify the functionality of the proposed nano-antenna have been investigated. Finally, the idea of an on-chip wireless transmission link based on transmitting and receiving HPRNAs has been developed and studied theoretically and numerically. The fabrication of the proposed nano-antenna can be done by the typical e-beam lithography (EBL) technique, which is easier than the complicated X-ray method because of its suitable aspect ratio.
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1. Introduction
The indispensable considerations of designing optical nano-antennas fed by plasmonic waveguides are impedance matching between the radiation part and waveguide feeding structure, high confinement factor, low propagation loss and miniaturization of the communication devices to enhance the speed of wireless communication and its radiation efficiency [1,2]. Obtaining the radiation characteristics by the excitation of surface plasmon polaritons (SPPs) oscillations to enable wireless communication is one of the functionalities of these nano-antennas, which are preferably designed using noble metals such as gold and silver [3] and utilizing the properties of VO2 [4]. However, at the optical telecommunication wavelengths these metallic nano-antennas have high propagation loss and low effective mode index [5]. In order to mitigate these limitations, hybrid plasmonic waveguides (HPWs) gained attention due to their desirable optical properties such as tight light concentration into the low index dielectric layer and significantly subsiding the propagation loss [6].
HPW configuration consists of a low-index layer sandwiched between the metal-cap and high-index dielectric layer and supports transmission of both transverse electric (TE) and transverse magnetic (TM) modes, which can effectively confine them separately in dielectric layers with high confinement factor [7]. Hybrid plasmonic nano-antennas (HPNAs) have attained considerable heed in recent years as one of the crucial components for optical wireless communications, which to precisely match the impedance would be inlay fed by HPWs. For the first time, the idea of HPNAs proposed by Yousefi et al. [8] based on introducing a waveguide-fed patch HPNA with the gain of 5.6 dB at the frequency of 193.5 THz and narrow bandwidth of 15 THz. The concept of multilayer HPW structure has been used by Sharma et al. [9] to enhance the gain of patch HPNA to 8.3 dB. In order to improve the bandwidth to nearly 250 THz, the configuration of Vivaldi nano-antenna [10] has been introduced. Suffering silicon-on-insulator (SOI) and polymer based HPW components from their shortage of monolithic integration capability with active devices such as laser and photodetector at optical frequencies is a critical bottleneck to develop integrated hybrid plasmonic circuits. In order to address this challenge, InP-based nano-antenna has been proposed [11], since InP-based technology offers great potential of monolithic integration of active and passive devices [12]. Moreover, a multiband horn nano-antenna with the gains of 4.8, 7.3 and 4.7 dB at the frequencies of 193.5, 229 and 352.9 THz has been reported [13]. However, due to its low performance with rectangular cross-section, Khodadadi et al. have utilized the idea of circular cross section to propose a high gain HPNA with the total efficiency and bandwidth of 92.89% and 40 THz, respectively, at 193.5 THz [14]. The interesting concept of circularly polarized L-hexagonal shaped patch HPNA has been introduced but needs further investigations to flourish this idea in future researches [15]. For the first time, the idea of multi-user access in wireless transmission system has been developed by designing a super mode HPNA [16]. This amazing concept has been completed by utilizing the vertical graphene quantum well HPNA with the aim of controlling the accessibility of users through the features of graphene as an epsilon-near-zero and absorptive/transparent material [17].
The future of integrated circuits will require wireless chip-to-chip communication to overcome the bottlenecks caused by wired connections. The indispensable part of each wireless communication system is wideband antennas with compact size, ultra-high gain and efficiency, which allow high wireless data capacity of several terabits per second [18]. Therefore, future of advanced chip-to-chip communication is more related to optimize wireless transmission link, which shows the importance of proposing high performance HPNAs.
In this paper, a complementary metal-oxide semiconductor (CMOS) compatible hybrid plasmonic rhombic nano-antenna (HPRNA) with dielectric director is introduced. The idea of utilizing dielectric director is exploited for the first time to obtain a totally horizontal radiation pattern that is necessary for wireless transmission link in order to develop the concept of chip-to-chip communication. By choosing HPW with three layers of silver, hydrogen silsesquioxane (HSQ), and silicon, the propagation length, effective mode index and figure of merit of 94.4 µm, $8.41 \times {10^{ - 14}}$ and $5.87 \times {10^8}$ are obtained, respectively, at the frequency of 193.5 THz. Investigation of far-field characteristics of HPRNA shows the gain and directivity of 10.3 dB and 10.5 dBi at 193.5 THz, respectively, with 3 dB beamwidth of 43.5° and side lobe level of −11.9 dB. The functionality of nano-antenna as the receiver and transmitter to create a wireless link is investigated numerically and theoretically by the finite element method (FEM) and Friis equation, respectively. To obtain the best performance of the HPRNA, the optimized structural parameters have been selected that study of their effects verifies our acclaim. Finally, we have shown that the proposed HPRNA is quite tolerant to practical fabrication errors.
The paper is organized as follows. In section 2, the performance of HPRNA will be discussed in detail. The wireless point-to-point inter link will be studied in section 3. The fabrication feasibility will be investigated in section 4, and the paper would be concluded in section 5.
2. HPRNA with dielectric director
The three-dimensional (3D) schematic and top views of the proposed HPRNA are shown in Fig. 1. The utilized HPW consists of three layers of silver, HSQ, and silicon. These layers are placed on a substrate consisting of two layers of silica and silicon. The thicknesses of these layers are chosen based on the technological challenges and limitations to be compatible with the SOI technology in order to avoid complexity of fabrication process. In addition, the silicon substrate is a bulk material with the thickness of the order of hundreds of micrometers in photonic integrated circuits (PICs), which can be considered as an infinite layer in comparison to the desired wavelength of 1550 nm (193.5 THz) [17]. Consequently, the thickness of hSi = 800 nm is considered for the silicon layer to reduce the computation time and memory requirements. Also, the silica layer is thick enough to prevent damage to the silicon wafer, which is one of the most common substances used to develop PICs. The relative permittivities of HSQ and silica layers are ${\varepsilon _{HSQ}} = 1.96$ and ${\varepsilon _{Si{O_2}}} = 1.96$, respectively. Moreover, the relative permittivities of sliver and silicon layers are extracted from Johnson-Christy and Palik data [10,19]. It is worth mentioning that silver is chosen as a metal cap layer due to the smallest total damping rate (Γ= 0.02 eV), lowest loss, much better SPP confinement at telecommunication wavelengths, highest SPP quality factor $({{Q_{SPP}} = {{{\varepsilon^{\prime}}_m{{(\omega )}^2}} / {\varepsilon^{{\prime\prime}_{m}}(\omega )}}} )$ in visible and near-infrared regions, and low fabrication cost [20]. Furthermore, HSQ, an amorphous structure similar to silica with a good adhesion on silicon wafers has some advantages such as high uniformity, high etching resistance, high resolution, and minimum line edge roughness [21]. Hence, it is a good candidate for the low-index layer of the proposed HPW.
Fig. 1. (a) The 3D perspective and (b) top view of the proposed HPRNA. (c) Schematic cross-sectional view of the single mode HPW. The geometrical dimensions are ${L_{wg}} = 250\,\,\textrm{nm}$, ${L_a} = 915\,\,nm$, ${L_b} = 554\,\,\textrm{nm}$, ${L_R} = 829\,\,\textrm{nm}$, ${W_a} = 170\,\,\textrm{nm}$, ${W_b} = 70\,\,\textrm{nm}$, ${W_{wg}} = 170\,\,\textrm{nm}$, ${h_m} = 150\,\,\textrm{nm}$, ${h_L} = 25\,\,\textrm{nm}$, ${h_H} = 400\,\,\textrm{nm}$, ${W_{sub}} = 1600\,\,\textrm{nm}$, ${h_{Si{O_2}}} = 500\,\,\textrm{nm}$, ${h_{Si}} = 800\,\,\textrm{nm}$, and ${L_{sub}} \times {W_{sub}} = 1560 \times 1600\,\,\textrm{n}{\textrm{m}^\textrm{2}}$.
Distribution of TM mode profile and electric field amplitude of the proposed HPW obtained by FEM and theoretical analysis [16] are illustrated in Fig. 2. It shows that the excited mode is confined tightly in the low-index HSQ layer at the frequency of 193.5 THz. In order to confirm the enhancement of propagation length $({{L_p} = {\lambda / {4\pi {{n^{\prime\prime}}_{eff}}}}} )$ of the proposed HPW in comparison to the plasmonic waveguides, its spectrum with the real part of the effective refractive index $({{{n^{\prime}}_{eff}}} )$ are depicted in Fig. 3. The obtained propagation length is 94.4 µm at 193.5 THz that indicates SPPs can propagate without the sharp damping up to 94.4 µm. In addition, the obtained effective mode index $\left( {{A_{eff}} = \frac{{\int\!\!\!\int {W(x,y)} \,dxdy}}{{\max \{{W(x,y)} \}}}} \right)$ and figure of merit $\left( {\textrm{FOM} = {{{L_P}} / {\sqrt {{{{A_{eff}}} / \pi }} }}} \right)$ of the proposed HPW are $8.41 \times {10^{ - 14}}$ and $5.87 \times {10^8}$, respectively, where $W(x,y)$ is the energy density per unit length flowed along the direction of propagation [22]. These results confirm that HPW has a better performance compared to the similar plasmonic waveguide.
Fig. 2. (a) Distribution of TM mode profile and (b) electric field amplitude of the proposed HPW along the y direction (∣Ey∣) when x = 0 at 193.5 THz. The electric field amplitude is obtained based on both numerical and theoretical approaches.
Fig. 3. Spectra of the real part of the effective refractive index and SPPs propagation length of the proposed HPW based on the numerical simulation.
The optimization of the proposed HPRNA performance is approached by considering two main goals: propagation length and antenna radiation performance, including gain, efficiency, and horizontal radiation pattern. In order to achieve a long propagation length, the waveguide without the radiation part is designed as the first step. The width and height of each layer are optimized using the CST Microwave Studio software optimization tools to obtain the effective refractive index, which is critical to achieve this goal. In the second step, after obtaining the optimized propagation length, the performance of the proposed HPRNA is further improved by setting goals for attaining the impedance matching (S11<−10 dB), gain (G > 10 dB), efficiency (e > 90%) and horizontal radiation pattern. The optimization process involves adjusting various parameters of the nano-antenna design, such as dimensions and positions of different components to achieve the desired performance criteria.
In order to investigate the far-field characteristics of the proposed HPRNA, the return loss spectrum (S11) for controlling the impedance matching between the HPW and flared radiation part should be studied. The matching is achieved for only the real component of the impedance, because the imaginary part due to the plasmonic losses is much smaller than the real part at the resonance frequency of 193.5 THz. Therefore, the reflected wave is expected to be minimal. Examination of the reflection coefficient spectrum of Fig. 4(a) shows that the impedance matching occurs in the frequency range of 190.96 to 212.39 THz. Therefore, it is possible to study the antenna performance in this interval because the gain and directivity of HPRNA are valid in this range, as depicted in Fig. 4(a). The maximum gain and directivity are 9.87 dB and 10 dBi at 193.5 THz, respectively. According to the radiation pattern of Fig. 4(b), the main lobe direction is shifted about −35° relative to the z-axis at, which is not suitable for inter/intra-chip application.
Fig. 4. (a) The reflection coefficient, gain and directivity spectra and (b) 3D radiation directivity and gain pattern of HPRNA without director at 193.5 THz, which are obtained based on FEM simulation.
The concept of rhombic radiating part is used to compensate low directivity, high side lobes, impedance mismatch between waveguide and free space and control the main beam angle of a single long HPW, which leads to reflecting excited electromagnetic lightwave to the source [23]. In such these nano-antennas, the aperture angle of radiation part plays an important role in controlling the main beam width, gain and direction of radiated pattern. If the flaring angle of the tapered opening is close to 90°, the mismatch between the flare part and the free space increases, because it plays as an opening HPW, which results in decreasing the far-field performance of the proposed HPRNA drastically. In this regard, based on the results in Ref. [23], we estimate the flare angle and then it is optimized to be $\theta =$36°. In Table 1, the effect of changing the flare angle on far-field characteristics of the HPRNA has been investigated, which proves the best performance can be attain when $\theta =$36°. It must be noted that by further increasing the flare angle from 46° to 90°, the foot-print of the proposed nano-antenna should be changed. Therefore, to show the major impact of changing θ on the antenna performance, this crucial geometrical parameter and its functionality have been studied only until $\theta =$46°. Besides, there is a major reason behind the investigation of θ without changing the antenna foot-print, because the impedance matching (S11<−10 dB) has not been satisfied.
Table 1. Studying the effect of flare angle on the far-field characteristics of proposed HPRNA.
The length of flared radiation part of the HPRNA is another effective parameter in controlling the gain and directivity of nano-antenna, which is chosen based on the idea in Ref. [9] and then the best length is obtained with the help of optimization method. The reflection coefficient spectra of Fig. 5(a) show that although for La = 815 nm, the bandwidth of nano-antenna is about 40 THz, but it does not have efficient performance at the target frequency of 193.5 THz. Also, regarding to the obtained results of Figs. 5(b) and (c), the best gain and directivity can be reached by considering La = 915 nm.
Fig. 5. (a) The reflection coefficient, (b) gain and (c) directivity spectra of the HPRNA versus the variations of the flare length (La).
To address the issue of tilted radiation pattern, the idea of dielectric director is proposed, as shown in Fig. 6(a). Using Si director not only leads to the modification of tiled radiation pattern to the horizontal one, but also it enhances the gain and bandwidth of HPRNA, according to Fig. 6(b), which is useful for point-to-point connection in wireless links and networks. The bandwidth of the proposed HPRNA with dielectric director is 40 THz. Furthermore, the maximum gain and directionality are 10.3 dB and 10.5 dBi at 193.5 THz, respectively, with the total efficiency of 95.50%.
Fig. 6. (a) 3D perspective view of the HPRNA with dielectric director and (b) its reflection coefficient, gain and directivity spectra. The dimensions of director are ${W_d} = 200\,\,\textrm{nm}$ and ${L_d} = 1400\,\,\textrm{nm}$ and the other dimensions are the same as Fig. 1. The distance between the director and antenna is near to zero to obtain totally horizontal radiation pattern.
The 3D radiation pattern of HPRNA with Si director is plotted in Fig. 7. It can be seen that a completely horizontal radiation pattern with 3 dB beamwidth of 43.5° and side lobe level of −11.9 dB are attained. As it is mentioned earlier, the director role is to increase the gain and directivity of HPRNA, reduce the effect of surface current caused by the substrate and correct the displacement of the main beam angle. Therefore, the director should be able to receive the cone-shaped patterns that radiate from each antenna arms in the near-field region of the proposed HPRNA. Based on this concept, at the beginning of the simulation, the director length is assumed to be equal to the aperture of the HPRNA, and then its optimal length is selected by determining the objective function that is achieving the horizontal radiation pattern. Moreover, another challenge is the director thickness, which is considered equal to the thickness of the proposed HPW structure and then the optimum thickness is obtained by controlling the objective function to achieve the gain of 10.3 dB.
Fig. 7. 3D radiation directivity and gain pattern of the proposed HPRNA with Si director at 193.5 THz, which shows the advantage of utilizing director to create a horizontal radiation pattern.
In this regard, there is an intuitive explanation for why a dielectric director can solve the tilted radiation pattern issue in the HPRNA design. When an electromagnetic wave is incident upon a dielectric material with a specific refractive index, the direction of the wave is bent or refracted at the interface between two materials. This bending effect can be used to control the directionality of the radiation pattern emitted by the antenna. In the case of a tilted radiation pattern, the wavefronts of the electromagnetic radiation are not perpendicular to the surface of the antenna, leading to a non-uniform distribution of the radiated power in different directions. By introducing a dielectric director with a specific refractive index and shape, the wavefronts can be refracted to achieve a desired radiation pattern. In essence, the dielectric director acts as a lens for the electromagnetic radiation, focusing it in a particular direction and mitigating the tilted radiation pattern issue.
The results of studying the impact of length and width of Si director on the HPRNA performance are shown in Tables 2 and 3, respectively. It is obvious that by setting the director not only the main lobe direction is modified, but also by increasing the length from 1200 to 1400 nm, the gain, directivity and bandwidth are improved significantly. The more increase of the director length leads to the destructive effect on the HPRNA functionality. The variation of director width reveals that the modification of main lobe direction is related strongly on it. By increasing the width both gain and directivity are enhanced and the best far-field response is obtained for Wd = 200 nm with the gain, directivity and bandwidth of 10.3 dB, 10.5 dBi, and 40 THz, respectively.
Table 2. The Effect of varying the director length on the HPRNA performance.
Table 3. The Effect of varying the director width on the HPRNA performance.
2.1 Comparison between the suggested nano-antenna and previous works
In order to demonstrate the advantages and disadvantages of the proposed HPRNA, a comparison should be made with other HPW nano-antennas that take into account various factors, including but not limited to gain, efficiency, propagation length, radiation pattern, and manufacturing complexity. For the first point, high gain and efficiency are important for creating point-to-point wireless links because they determine the strength and quality of the received signal. A high gain antenna has a narrow beamwidth, which allows for more accurate targeting of the signal to the receiver and reduces interference from other sources. This results in a stronger signal with less noise and distortion, which leads to better communication performance. Efficiency is also a critical consideration as it measures how much of the transmitted power is actually radiated as electromagnetic waves. An antenna with high efficiency radiates more power and requires less input power to achieve a given level of output, which is especially important for wireless communication systems that operate on battery power or have limited power resources. Therefore, both high gain and efficiency are important for achieving a reliable and robust point-to-point wireless link, particularly in applications that require long-range communication, such as telecommunication networks, satellite communication, and remote sensing. These two factors have been compared as follows.
The gain of proposed HPRNA compared to the patch [8], Vivaldi [10], bow-tie [11], and horn [13] antennas has been improved 4.6, 5.2, 1.03, and 5.5 dB at the frequency of 193.5 THz, respectively. Also, in comparison to bow-tie HPW-based nano-antenna [11] the obtained propagation length increases almost 10 times. On the other hand, for proposing on-chip nano-antenna for wireless transmission link, the horizontal radiation pattern is necessary. In comparison to the patch nano-antenna with bidirectional vertical radiation pattern and 15 THz bandwidth [8], by utilizing the dielectric director, the problem of the squint beam is solved and the bandwidth is enhanced to 40 THz. Moreover, the problem of multi-bandwidth horn nano-antenna [13], which could not be used in multi-channel structures has been solved. Compared to the super-mode nano-antenna [16] with the efficiency of close to 9%, the efficiency of proposed nano-antenna is more than 95%.
Secondly, an essential factor for achieving a point-to-point wireless link is a horizontal main lobe, which some previous works in the literature lack compared to our work [8–10,13–16,24–27]. It is because horizontal main lobe allows for directional communication between two points, which can improve the signal-to-noise ratio and reduce interference from other sources. Furthermore, an important feature that some works do not pay sufficient attention to is the long propagation length of the HPW, which is a critical consideration for achieving successful long-distance wireless communication [24–29].
Moreover, the fabrication feasibility of a HPW is important because it affects the practicality and cost of producing the waveguide. HPW is composed of both metallic and dielectric materials, which can make its fabrication more challenging than traditional waveguide. Fabrication techniques such as EBL and focused ion beam (FIB) milling are commonly used to create the necessary nanoscale features of HPWs. However, these techniques can be expensive and time-consuming. In addition, the materials used to construct the waveguide can also impact its fabrication feasibility. For example, certain metals used in plasmonic structures may be difficult to work with due to their high melting points or chemical reactivity. Similarly, the choice of dielectric material can also impact the fabrication, as some materials may require specialized processing steps or have limited compatibility with other materials. Overall, ensuring the fabrication feasibility of a HPW design is crucial for ensuring that it can be produced reliably and at a reasonable cost. In the following the fabrication feasibility of the proposed HPRNA is compared with previous works.
Choosing the rectangular cross-section to design the HPRNA is one of the most important superiorities compared to the circular one [14] in order to reduce the fabrication process complexity and improve the propagation length more than 12 times. Another advantage of the proposed HPRNA is related to its aspect ratio in comparison to the previous proposed horizontal nano-antennas that leads to utilizing typical EBL technique to fabricate it instead of complicated X-ray method [30,31]. In addition, the proposed nano-antenna has linear polarization, but the polarization of L-hexagonal shaped patch HPNA introduced by Mohanta et al. is circular [15]. All these points reviewed are summarized in Table 4.
Table 4. Comparison of the results of our proposed nano-antenna with previous works at 193.5 THz.a
3. Wireless point-to-point inter link
The considerable idea of proposing HPRNA is its ability to create an optical wireless link in order to transmit the electromagnetic power from the transmitting nano-antennas to receiving nano-antenna because of its high gain, high efficiency and horizontal radiation pattern. Consequently, the performance of the proposed HPRNA has been investigated as an on-chip wireless link, as plotted in Fig. 8.
Fig. 8. 3D Schematic view of wireless link which consists of two HPRNAs as transmitter and receiver. dlink is the distance between the transmitting and receiving antennas.
The ratio of the received power $({{P_r}} )$ to the transmitted power $({{P_t}} )$ can be calculated from the Friis equation [1]:
The electric field distribution of the wireless transmission link (Fig. 9(a)) shows that the amplitude of the radiation power from the transmitting nano-antenna is gradually reduced due to propagation loss. The guided power is recollected by the receiver and it is concentrated and transferred in the layer with lower refractive index. The attained results for the ratio of the received power to the transmitted power by the Friis equation (Eq. (2)) and FEM simulation (Fig. 9(b)) are −7.27 dB and −6.76 dB, respectively.
Fig. 9. E-field distribution between two HPRNAs at 193.5 THz in xy-plane and (b) the spectrum of the ratio of received power to transmitted powers (S21) of point-to-point wireless link based on the FEM simulation.
4. Fabrication feasibility and excitation setup
Here, we would like to investigate the fabrication process and fabrication error tolerance to show the fabrication possibility of the suggested HPRNA. Knowing about the tolerances in each fabrication method and its metrology is the most import prior section of experimental setup. It is still impossible to obtain a structure that is accurate to within 1 nm in every dimension, as well as to perfectly characterize that structure [16]. Therefore, we need to take in account that the proposed nano-antenna to be insensitive to these kinds of fabrication imperfections with tolerances to dimension variations up to at least 5% [16]. Considering such these important practical issues will also greatly enhance the yield of nano-antenna. To investigate the fabrication error tolerance and its effect on the nano-antenna functionality, some important geometrical parameter variations are studied, which their results are given in Table 5.
Table 5. Fabrication errors of some geometrical parameters of the HPRNA at 193.5 THz.
From Table 5, it can be observed that the maximum error is related to the flare angle, which the FIB technique can mitigate this imperfection. The obtained results show an acceptable fabrication tolerance error. To excite the plasmonic mode in the HPW a single mode fiber should be used. The fiber output is at first converted into the fundamental TM mode of a silicon strip waveguide by a TM polarized grating couplers [32]. So, to facilitate an efficient coupling between the TM mode in the silicon strip and the hybrid plasmonic mode in the HPW, a tapered coupler should be utilized. In order to fabricate the proposed nano-antenna, the waveguides should be defined by EBL and inductive coupling plasma reactive ion etching (ICP RIE). Then the sample is spin coated with a HSQ layer of 30 nm thick. After that the 100 nm thick metal (Ag) layer can be patterned by lift-off technique.
Finally, we have investigated the effect of an inclined wall with an angle of 4°, as shown in Fig. 10. It is obvious that the inclined wall has a minor effect on the radiation pattern of the proposed HPRNA. In addition, the maximum propagation length is obtained 95.5 µm at 193.5 THz. The propagation length increases in comparison to the rectangular cross section, because the inclusion of the inclined wall improves the confinement factor at the low index layer.
Fig. 10. (a) Schematic view and (b) 3D radiation pattern of the proposed HPRNA with considering the effect of inclined wall
5. Conclusion
In summary, a HPRNA with dielectric director has been proposed to design an on-chip wireless transmission link. The bandwidth and total efficiency of this nano-antenna are 40 THz and 95.5%, respectively. The impacts of physical parameters and functionality of the proposed nano-antenna have been investigated completely to confirm that not only ±5% fabrication tolerance does not have critical effect on the nano-antenna performance, but also nano-antenna dimensions have been optimized to have the best radiation pattern feature. Moreover, the performance of wireless transmission link, which is composed of two transmitting and receiving nano-antennas with the low-index HSQ layer has been studied based on the FEM and Friis equation.
Funding
Iran National Science Foundation (Grant No. 98019891).
Acknowledgment
The authors would like to thank the Iran National Science Foundation (INSF) under the grant No. 98019891 for financial support of this project.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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