Nanolink parameters used in simulations. All parameters are in nanometer (nm).
In this work, we present a theoretical analysis of wireless optical nanolinks formed by plasmonic nanoantennas, where the antennas considered are Yagi-Uda and cylindrical nanodipoles made of Au. The numerical analysis is performed by the finite element method and linear method of moments, where the transmission power and the near electric field are investigated and optimized for three nanolinks: Yagi-Uda/Yagi-Uda, Yagi-Uda/dipole and dipole/dipole. The results show that all these case can operate with good transmission power at different frequencies by adjusting the impedance matching in the transmitting antennas and the load impedance of the receiving antennas.
- wireless optical nanolink
- power transmission
The electromagnetic scattering of metals in optical frequency region possesses special characteristics. At these frequencies, there are electron oscillations in the metal called plasmons with distinct resonant frequencies, which produce strongly enhanced near fields at the metal surface. This effect can be analyzed using Lorentz-Drude model of the complex dielectric constant. The science of the electromagnetic optical response of metal nanostructures is known as plasmonics or nanoplasmonics [1, 2].
One subarea of nanoplasmonics is the field of optical nanoantennas, which are metal nanostructures used to transmit or receive optical fields [3, 4, 5]. This definition is similar to that of conventional radio frequency (RF) and microwave antennas. The main difference between these two regimes (RF-microwave and optical) is due to physical properties of the metals at optical frequencies where they cannot be considered as perfect conductors because of the plasmonic effects . Comprehensive reviews on optical antennas have been presented in [6, 7, 8, 9, 10, 11]. In these works, the authors described recent developments in calculation of such antennas, their applications and challenges in their design. In Figure 1, we present some examples of fabricated nanoantennas.
Optical nanoantennas have received great interest in recent years in the scientific community due to their ability to amplify and confine optical fields beyond the light diffraction limit . With this characteristic, it is possible to apply in several areas, such as nanophotonics, biology, chemistry, computer science, optics and engineering, among others [6, 7, 12]. In addition, these studies were expanded due to the development of computational numerical methods and innovations in nanofabrication techniques, such as electron beam lithography, colloidal lithography and ion beam lithography .
Optical wireless nanolinks with nanoantennas can be used to efficiently communicate between devices, significantly reducing the losses that occur in wired communication. Nanolinks with different geometries of nanoantennas were investigated in the literature [13, 14, 15, 16, 17]. In  the authors propose a broadband nanolink formed by dipole-loop antennas. The results showed that using this nanolink with dipole-loop antennas instead of conventional dipoles, it is possible to increase the operating bandwidth of the system to the range of 179.1–202.5 THz, which is within the optical range of telecommunications. In , a wireless nanolink formed by dipole antennas is compared to a wired nanolink formed by a waveguide, the study showed that the wireless link may work better than a plasmon waveguide in sending optical signal in nanoscale from one point to another, from a certain distance. In , a nanolink Yagi-Uda chip directives are proposed, the results show that the use of directional antennas increases the energy transfer (power ratio) and link efficiency, minimizing interference with other parts of the circuit. In , it is presented another wireless nanolink application formed by a transmitting nanoantenna Vivaldi and another receiver, to be used in chip, with that nanolink a high gain and bandwidth covering the entire spectrum of the C band of telecommunications. In , broadband nanolinks were analyzed using horn and dipole type optical nanoantennas, where the horn antenna had better performance, because better energy transfer at the nanolink and greater bandwidth were obtained in relation to the dipole link. These studies used identical transmitting and receiving antennas, and showed the feasibility of using wireless communication in the nanophotonics.
In this work, we present a comparative analysis of nanolinks formed by equal and different transmitting and receiving nanoantennas. The antennas used are Yagi-Uda and dipole. The numerical analysis is performed by the method of moments (MoM)  and the finite element method (FEM) through the software COMSOL Multiphysics . In this analysis, the transmission power and the near electric field are investigated for three nanolinks: Yagi-Uda/dipole, Yagi-Uda/Yagi-Uda and dipole/dipole. This work is organized as follow: Section 1 is the introduction, Section 2 presents the description of nanolinks, Section 3 presents the numerical model used in the analysis, Section 4 contain the numerical results, and Section 5 are the conclusions.
2. Description of nanolinks
In this work, three models of nanolinks are proposed and analyzed. The first is a nanolink formed by dipole/dipole antennas (Figure 2, without reflector and directors), the second by Yagi-Uda/dipole antennas (Figure 2) and the third by Yagi-Uda/Yagi-Uda antennas (Figure 2, with the receiving antenna equal to the transmitting antenna).
The geometry of the Yagi-Uda/dipole nanolink is presented in Figure 2, where a voltage source
3. Numerical model
3.1 Method of moments
The linear MoM presented here is based in the linear current approximation with an equivalent surface impedance model of the cylindrical conductors, with sinusoidal test and base functions . The method will be explained for the particular example of a single dipole radiating in a free space, composed by plasmonic cylindrical elements made of gold.
Figure 3 shows the geometry of the original problem, the equivalent MoM and circuit models of the nanodipole. In this figure,
In the radiation problem of Figure 3, the gold material of the antenna is represented by the Lorentz-Drude model for complex permittivity
where the parameters in this equation are as follows :
The losses in metal are described by the surface impedance
being and . The boundary condition for the electric field at the conductor surface is , where is a unitary vector tangential to the surface of the metal, is the scattered electric field due to the induced linear current
The integral equation for the scattered field along the length
where is the free space Green’s function, and is the distance between source and observation points. The numerical solution of the problem formulated by (1)–(3) is performed by linear MoM as follows. Firstly, we divide the total length
The radiated power can be obtained by
3.2 Finite element method
The nanolinks of Figure 3 were also analyzed numerically by FEM. Figure 5a shows the mesh of the nanolink of Figure 2 modeled in the COMSOL, where the antennas are in a spherical domain of air, with scattering absorbing condition (PLM) applied at their ends. Figure 5b shows an enlarged image of the Yagi-Uda nanoantenna mesh and its surroundings.
4. Numerical results
4.1 Isolated antennas in transmitting mode
In this section, the transmitting antennas Yagi-Uda and dipole (Figure 2 without reflector and directors) are analyzed separately. For this analysis, the values of the antennas parameters are those shown in Table 1, where with these values the main resonances are in the frequency range of 100–400 THz considered. The parameters of the isolated dipole are based on  and those of the elements of the Yagi-Uda antenna were chosen so that the reflecting element was larger than the dipole and the smaller dipole directors. In Table 1,
Figure 6 shows the input impedance (
Also, the input impedances of the antennas are calculated for two situations, the first with the antennas in the free space (without substrate) and the second on a SiO2 substrate with a permittivity of 2.15.
Comparing the input impedance result between the Yagi-Uda and free-space dipole antennas, it is noted that the first two resonant frequencies are close, which shows that the directors and reflectors do not significantly affect the original resonant frequencies of the isolated dipole. The main differences between these two transmitting antennas are observed near the frequencies of 175 and 260 THz, which correspond physically to the dipole resonances of the reflector and directors, respectively. These resonances can be observed in the distributions of currents in these frequencies, which are not shown here.
Figure 6 also shows the effect of the substrate in the input impedance and resonant properties of the antennas. It is observed that by placing the antennas on the substrate, their resonances are shifted to smaller frequencies in relation to the antennas in the free space. This effect of the substrate is similar to that observed in antennas in the microwave regime .
Figure 7 shows the results of directivity (
Figure 8 shows the 3D far field gain radiation diagrams of the Yagi-Uda and dipole antennas, calculated at the frequency of 240 THz. It is observed that the maximum gain of the Yagi-Uda (
4.2 Nanolinks analysis
In this section, we present the results obtained in the analysis of the dipole/dipole nanolinks (Figure 2, without reflector and transmitter directors), Yagi-Uda/dipole (Figure 2) and Yagi-Uda/Yagi-Uda (Figure 2, with the receiving antenna equal to the transmitting antenna) for the frequency range of 100–400 THz. The parameters used for the receiving antennas are same as those of the transmitting antennas, with
Figure 9 shows the power transmission in dB (or power transfer function) for the three nanolinks, calculated by the ratio between the power delivered to the
Figure 10 shows the magnitude and phase of the electric near field, which is defined by
It was presented in this work, a comparative analysis of nanolinks formed by Yagi-Uda and dipole plasmonic nanoantennas, where was investigated the power transmission for Yagi-Uda/Yagi-Uda, Yagi-Uda/dipole and dipole/dipole nanolinks types. These nanolinks were numerically analyzed by method of moments and finite element method. The results show that the Yagi-Uda/Yagi-Uda nanolink presents a small improvement in power transmission, at some frequency points, in relation to the other cases. In addition, the three links can operate with good power transmit at different frequency points, varying the load impedance of the receiving antenna, which is of great importance for future applications in nanoscale wireless communication. In future work, we intend to feed these nanolinks by more realistic sources, such as gaussian beams, to verify their influence on power transmission results.
The authors would like to thank the Mr. Mauro Roberto Collato Junior Chief Executive Officer of the Junto Telecom Company for the financial and emotional support to this project.
Conflict of interest
The authors declare that there is no conflict of interests regarding the publication of this work.