We present in this work a simple and efficient technique to analyze cylindrical plasmonic nanoantennas. In this method, we take into account only longitudinal current inside cylindrical structures and use 1D integral equation for the electric field with a given surface impedance of metal. The solution of this integral equation is obtained by the Method of Moments with sinusoidal basis functions. Some examples of calculations of nanoantennas with different geometries and sources are presented and compared with the commercial software Comsol 3D simulations. The results show that the proposed technique provides a good precision in the near-infrared and lower optical frequencies 100–400 THz.

Optical antennas are metal nanostructures used to transmit or receive optical fields [

Conventional 3D techniques, for example, Green’s tensor method [

The first application of the surface impedance integral equation (SI-IE) for analysis of cylindrical optical antennas was presented in [

In [

In this work, we present an efficient and simple alternative technique to analyze metallic cylindrical nanoantennas. The method is a simplified version of that presented in [

The method is based on the linear Method of Moments (MoM) with sinusoidal basis functions [

Cylindrical plasmonic nanocircuit composed of voltage source, optical transmission line, and nanodipole. (a) Geometry of the problem. (b) Discretization used in MoM model.

Figure

In the radiation problem of Figure ^{15} s^{−1}, ^{14} s^{−1}, ^{14} s^{−1}, and ^{14} s^{−1}. This model is a good approximation with experimental data for wavelengths _{01} of infinite long cylindrical imperfect conductor [

The boundary condition for the electric field at the surface’s conductor of the circuit in Figure

Numerical solution of the problem formulated by (

Sinusoidal current element in one segment.

Substituting (

Substituting (

Local coordinate system of one generic sinusoidal current segment of (

Based on the theory presented in the previous section, we developed a MoM code in Matlab to analyze the nanocircuit shown in Figure

The developed MoM code can be used to analyze the near field resonances of nanorods excited by a plane wave. To this end, we modify only the geometry and the source of the original problem (Figure

Normalized electric field near single and two nanorods at point

For the case of the single nanorod in Figure

Resonant wavelength of

Figures

Input impedance of isolated nanodipole with

Input impedance of nanocircuit with

The results presented in these figures show a good agreement between the two methods. However, the MoM method results in smaller computational costs in terms of required memory and processing time. In the MoM model, one uses 1D current elements approximation for cylindrical conductors instead of 3D current elements inside the conductor in Comsol simulations. Also, the MoM discretizes only the conductors, and the Comsol discretizes the conductors and the domain around the conductors. This is why the MoM model requires a reduced number of unknown elements in the entire problem and, consequently, reduced memory and processing time in comparison with the Comsol simulation. For example, in Figure

In both methods (MoM and Comsol), we have carried out all the simulations in 3D surroundings. In the MoM model, we do not need radiation boundary condition because this method already takes into account this condition in the free space Green’s function. In the Comsol method, we used a spherical domain with PLM in the external boundary to simulate the free space and the lumped port source to simulate a voltage source.

This section presents an example of impedance matching analysis of the nanocircuit shown in Figure

Discretization of simulated nanocircuit. Parameters are

To make a quantitative measure of the impedance matching, we calculate approximately the voltage stationary wave ratio (VSWR) near the dipole as

Voltage reflection coefficient

Current distributions along nanocircuit at frequencies

Normalized electric near field distributions at plane

The input impedance of the isolated nanodipole versus frequency presented in Figure

We presented a simple and efficient computational method to analyze cylindrical plasmonic nanoantennas. We described details of the method which is based on the linear Method of Moments with sinusoidal basis functions. The losses in the conductors were taken into account by equivalent surface impedance. Some examples of nanoantenna were simulated and compared with the results obtained by the Comsol software. These examples include nanorods illuminated by an incident plane wave, nanodipoles fed by a voltage source, and a nanocircuit composed of a voltage source, a two-wire optical transmission line, and a nanodipole.

Our results show that the proposed method is computationally simple and produces results with a good agreement with the Comsol simulations up to lower optical frequencies (

In future works we intend to modify our method to take into account transversal currents in the cylindrical conductors. It will allow one to apply the method at higher optical frequencies. Also, the method can be used for analysis and design of nanoantenna systems, composed of cylindrical elements, for example, arrays of nanodipoles. Also, the method can be used to make the input impedance matching of nanodipoles with optical transmission line in order to optimize the energy transfer from source to load.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported by the Brazilian agencies PROPESP/UFPA and FADESP.