3.1.

Dipole Length Study

For comparison purposes, the response of a gold dipole antenna as a function of frequency is analyzed for different dipole lengths (Fig. 1). Results show that the deviation from the expected resonant frequency from classical antenna theory increases with frequency. This happens due to the increase in the resistivity of gold at optical frequencies; this effect also allows the electromagnetic wave to penetrate within the resonant structure. This effect can also be modeled using an effective length for the resonant dipole.¹³

Fig. 1

Induced current as a function of frequency for gold dipoles with different lengths.

Table 1 shows the calculated resonant wavelength for five different dipole lengths. The resonant frequency was obtained by calculating the frequency at which the maximum current was induced in the whole dipole structure. The current responsivity was calculated as the ratio of the induced current and the optical power incident on the antenna. The optical power was obtained as the product of the irradiance and the receiving area of the antenna, which can be approximated by the resonant wavelength squared (${\lambda }_{\mathrm{res}}^2$), according to the experimental measurements.¹⁴

Table 1

Shift in resonance and current responsivity for different gold dipole lengths.

This discrepancy in the optimum length of the dipole for a given wavelength is of importance when designing resonant elements at infrared and visible frequencies. This scaling factor has to be revised when considering the effect of the substrate on the resonance of the element. When Seebeck nanoantennas are designed to scavenge thermal radiation coming from moderate temperature radiators (thermal engines, intercoolers, and so on), the temperature of the radiating element fixes the optimum wavelength of operation through the Wien displacement law: ${\lambda }_{\max }T=2898\mu \mathrm{m}·\mathrm{K}$. Therefore, this parametric study allows us to select the optimum dipole length for a given radiation temperature. When considering the resonant wavelength given in Table 1, we find that thermal radiator temperature ranges from room temperature to 760°C.

3.2.

Effect of Materials

In the case of Seebeck nanoantennas, the chosen materials affect the responsivity in two ways, the first due to the Seebeck coefficient of the materials used and the second by the ability of the material to induce currents due to the radiant flux incident on the nanoantenna. A parametric study involving different metals and a single dipole geometry was performed (see Fig. 2). In this case, the length of the dipole was fixed at $3\mu \mathrm{m}$, and several simulations were performed using different materials.

Fig. 2

Induced current by a linearly polarized plane wave on gold, copper, silver, titanium, and nickel dipoles as a function of frequency.

Table 2 shows the resonant wavelength and current responsivity of a $3\text{-}\mu \mathrm{m}$ dipole for five different materials. In this table, we see that the resonant wavelength varies according to the optical properties of the material used for the fabrication of the antenna, and therefore its responsivity. Again, an appropriate selection of materials is of importance to optimize the signal obtained from a Seebeck nanoantenna.

Table 2

Resonance and responsivity of a 3-μm dipole for different materials.

3.3.

Analysis of Different Antenna Geometries

Several geometries can be used for fabricating Seebeck nanoantennas. Their performance is strongly related to their dimensions and how the electric field and currents are generated. The final choice of the geometry will be related to the desired polarization selectivity and the level of the signal obtained from each geometry.

Figure 3 shows the induced current density for three different types of nanoantennas. From these results, we can see that the bowtie and square spiral nanoantennas show the highest induced current density in comparison with the dipole nanoantennas. Also, in Fig. 3, we can see how the bowtie configuration concentrates most of the induced current in the feed of the antenna, leaving the ends of the antenna arms almost without current. This uneven current distribution favors the Seebeck effect by concentrating the heat generated by Joule heating in a small area, where the hot terminal can be placed, and a region without current where the cold terminal could be placed.

Fig. 3

Induced current density ($\mathrm{A}/{\mathrm{m}}^2$) due to an incident plane wave on a (a) dipole nanoantenna, (b) bowtie nanoantenna, and (c) square spiral nanoantenna.

Table 3 shows the total induced current in the antenna for the three different geometries and the current responsivity taken as the induced current divided by the incident optical power.

Table 3

Resonant frequency, induced current, and current responsivity for different antenna geometries.

Figure 4 shows the induced current for the three geometries considered as a function of the frequency of the incident plane wave. From Fig. 4, it can be seen that the square spiral configuration has the widest bandwidth and the highest induced current of the three geometries. However, Fig. 3 shows that the geometry that can generate a higher temperature gradient is the bowtie geometry, which favors the thermoelectric effect in a Seebeck nanoantenna.

Fig. 4

Induced current by a linearly polarized plane wave on gold dipole, bowtie, and square spiral nanoantennas as a function of frequency.

3.4.

Thermal Analysis and Seebeck Responsivity

Once we have analyzed the role of the geometry, material, and shape in the response of optical antennas, we combine different metals in order to obtain their thermal response when the resonant structure is illuminated under optimum conditions. As we know, the key factor in Seebeck nanoantennas is the difference in temperature between the hot and cold junctions. In this section, we will pay special attention to the analysis of bimetallic antennas and their thermal behavior when a given irradiance is impinging on them. Therefore, an analysis of the best bimetal combination is necessary to propose the fabrication of devices.

Even though from the previous section, we see that the bowtie geometry is the one that generates a higher temperature gradient and would be the ideal geometry to enhance the thermoelectric effect on Seebeck nanoantennas, the material analysis was made with dipole antennas due to the simplicity of the simulations and the fact that the results obtained with these geometries would apply to any geometry.

Figure 5 shows the temperature increase as a function of the length of the antenna structure for different combinations of materials. Nickel was always chosen as one of the materials since it is the only one that has a negative Seebeck coefficient. Therefore, this material combined with another with a positive Seebeck coefficient would give the highest voltage output [Eq. (1)].

Fig. 5

Distribution of temperature across the dipole nanoantennas for different metals analyzed in this work.

Table 4 shows the difference in temperature calculated between the bimetallic junction and the open ends of the dipole antenna. The voltage response of the antenna was evaluated by using the Seebeck effect. The Seebeck coefficients were taken as bulk ($S_{\mathrm{Ag}}=S_{\mathrm{Au}}=S_{\mathrm{Cu}}=6.5\mu \mathrm{V}/\mathrm{K}$, $S_{\mathrm{Ti}}=7.2\mu \mathrm{V}/\mathrm{K},$ and $S_{\mathrm{Ni}}=-15\mu \mathrm{V}/\mathrm{K}$). Table 4 also shows the voltage responsivity of the Seebeck nanoantennas. The values given in Table 4 can be used to make a first-order approximation of the efficiency of these devices calculated as the power that can be extracted by a current flowing through the antenna due to a voltage difference given by $V_{\mathrm{OC}}$. The value of the efficiency obtained, considering a $100\text{-}\mathrm{\Omega }$ resistive load, which is a good match to the input impedance of a dipole antenna, would be around $1\times {10}^{-9}\%$, which is within the same order of magnitude as the efficiency obtained for antennas coupled to metal-insulator-metal diodes.⁶

Table 4

Difference temperature and voltage responsivity for Seebeck dipole nanoantennas with 3-μm length.

From Table 4, it can be seen how the combination of Ti and Ni produces a Seebeck signal that is the largest for the studied combination.