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This paper presents a broadband nanoantenna fed by a two-wire optical transmission line (OTL). The antenna is defined by a combination of a dipole and a loop, where only the dipole element is connected to the OTL. The analysis is fulfilled by the linear method of moments with equivalent surface impedance to model the conductors. Firstly, the nanoantenna alone is investigated, where the input impedance, current distribution, reflection coefficient, fractional bandwidth, radiation efficiency, and radiation pattern are analyzed. Then, the input impedance matching of this antenna with the OTL is considered. In this case the current, near field distribution, radiation pattern, and reflection coefficient are calculated for different geometrical parameters. The results show that the loop inserted in the circuit can increase the bandwidth up to 42% and decreases the reflection coefficient in the OTL to −25 dB.

Recently, accompanying the development of plasmonic technology, the study of antennas exceeded the microwave barrier, reaching the infrared and optical regions. In these regions, there is a profusion of possibilities and proposals of applications. These antennas are devices designed to transmit, receive, and manipulate optical fields in nanometric scale going beyond the diffraction limit [

Optical antennas can also be used in conjunction with plasmonic waveguides for designing highly integrated photonic signal processing systems, because plasmonic waveguides can efficiently handle optical fields in nanometric scale beyond the diffraction limit as well [

In this work, a theoretical analysis of a broadband nanoantenna in an optical nanocircuit is presented. The broadband nanoantenna is formed by a combination of a loop and a dipole antenna. It is connected to a two-wire optical transmission line. The nanoantenna is obtained by placing the electric nanodipole in the center of the rectangular loop with a power source connected to the nanodipole. This geometry was used due to its simplicity in manufacturing and calculus as compared, for example, with the geometries of [

The numerical analysis is performed via a simple and efficient computational method based on linear method of moments (MoM) [

This section presents the geometry of the problem and the model of the plasmonic nanocircuit by the MoM. In this model, the Lorentz-Drude model is used to represent the complex permittivity of the metal, which is used in the calculation of the surface impedance of the cylindrical conductors of the circuit. The linear MoM is used to solve the 1D integral equation of the electric field with linear approximation of the longitudinal current, sinusoidal basis functions, and test functions of rectangular pulse [

The nanocircuit structure is shown in Figure

Nanocircuit, consisting of a two-wire optical transmission line (OTL), a dipole antenna (straight dipole), and a loop antenna (rectangular).

For conducting the analysis of the nanocircuit shown in Figure

Top view of the cylindrical plasmonic nanocircuit.

Side view of the cylindrical plasmonic nanocircuit without OTL.

Gold is the material chosen to make the cylindrical nanostructures of the circuit considered in this work. It is represented by the complex permittivity model of Lorentz-Drude

We use the following boundary condition for the electric field on the surface of the linear conductor: _{01} mode [

The equation for the scattered electric field due the current on length

Substituting (

Figure

Discretization of nanocircuit, top view (

In this section, we discuss firstly the accuracy of the developed MoM code comparing our results with experimental data published in literature, then we analyze the nanoantenna separately from the nanocircuit, and, later on, the complete circuit will be investigated. Matlab codes were developed from the mathematical model presented in Section

In order to verify the accuracy of our MoM code, this section shows a comparison between a cylindrical gold nanorod (Figure

Extinction cross section normalized by the area of the geometrical cross section

Among the various experimental results [

Initially, the numerical results for a specific geometry with

Input impedance of the electric nanodipole as a function of frequency.

Figure

Input impedance of the composed nanoantenna as a function of frequency.

Figure

Radiation efficiency (

We can note in Figure

Figure

Radiation efficiency (

Figure

3D far field gain radiation pattern of the isolated dipole and composed antenna for the central frequencies 194.97 and 170.85 THz, respectively.

Table

Results of parametric analysis of the composed nanoantenna (calculated through Comsol).

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30 nm | 40 nm | 50 nm | 60 nm | 70 nm | ||

| 10 nm | | | | | |

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20 nm | | | | | | |

| | | | |

Input impedance of the composed nanoantenna for

Input impedance of the composed nanoantenna for

Radiation efficiency (

Radiation efficiency (

The results of Figures

In the next section, we consider an OTL connected to the composed nanoantenna for a quantitative analysis of the impedance matching of the OTL with the nanoantenna.

Figure

Normalized current distribution along the nanocircuit for

The electric field distribution in the plane

Figure

3D far field gain radiation pattern of the circuit for

To analyze the impedance matching of the OTL with the antenna, it is necessary to calculate the voltage reflection coefficient (|

Voltage reflection coefficient as a function of frequency; the parameters are

For the frequencies corresponding to these minimum voltage reflection coefficients for the case of the nanocircuit with loop, the current distribution in Figure

Current distribution in the nanocircuit for

Electric field distribution in plane

It can be observed in these figures (Figures

Figure

3D far field gain radiation pattern of the circuit for

Finally, a parametric analysis of the voltage reflection coefficient is shown in Figures

Voltage reflection coefficient

Voltage reflection coefficient

In this study, we analyzed one application of cylindrical broadband nanoantennas in plasmonic nanocircuits, where the circuit comprises a nanoantenna connected to a two-wire optical transmission line. The nanoantenna presents a combination of a loop and a dipole antenna. In the circuit modeling, the Lorentz-Drude model was used to represent the physical characteristics of the metal. The method of moments (MoM) was applied to find the solution of the 1D integral equation for the electric field with linear approximation of the longitudinal current, finite surface impedance to represent losses in the conductor, sinusoidal basis functions, and rectangular pulse for test functions. To validate the MoM model we compared a MoM simulation with an experimental result from [

Initially, the nanoantenna was investigated separately from the nanocircuit and then the complete circuit was investigated. In relation to the study of the isolated nanoantenna, the results show that the electromagnetic coupling between the antennas (dipole and loop) modifies the input impedance and increases the bandwidth of nanoantenna in comparison with the isolated electrical dipole. The best result for the nanoantenna bandwidth is 42%, and, in general, for all simulations, this bandwidth was within 33.2 <

The nanocircuit which combines the nanoantenna and OTL was also investigated, focusing on the input impedance matching between the OTL and the nanoantenna. The obtained results showed that the overall voltage reflection coefficient decreases with the inclusion of the rectangular loop, reaching a value of approximately −25 dB. A good impedance matching can be achieved in different frequency bands tuning the nanocircuit operating frequency by varying the width and length of the rectangular loop. Another important result is the far field gain radiation pattern of the circuit, where the shape of the pattern suggests that the circuit behaves as an array of two antennas spaced by the length

The analyses presented in this paper may be useful as guidelines for the design of efficient plasmonic optical nanocircuits for applications in nanophotonics and nanoelectronics.

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, CAPES, and CNPq.