Besides the electromagnetic characteristics, the thermal properties of the materials are mainly described by the thermal conductivity $\kappa $, its specific heat, $Cp$, and the mass density, $d$. In Sec. 2, we have seen that the system behaves as stationary. Therefore, $Cp$ and $d$ are not included as design parameters. Figure 2 shows the spectral variations of the skin depth for several metals. We can see that Ti shows the largest value of skin depth. This means that the electric field penetrates deeper into the metal, building up electric currents within it. This property will be fully exploited when simulating the overall response of devices fabricated in Ti. On the contrary, Au is the metal showing the thinnest skin depth. On the other hand, skin depth will also affect the optimum resonant length of the dipole. It is known that the length of the dipole, $l$, at which the maximum response is obtained, $loptimum$, depends on the value of the index of refraction of the surrounding materials. This has been demonstrated by Novotny^{24} using the concept of effective wavelength, $\lambda eff$. This is the wavelength at which the antenna resonates, and follows the linear relation: Display Formula
$\lambda eff=n1+n2\lambda 0\lambda p,$(6)
where $n1$ and $n2$ are constants derived from material and geometric characteristics, $\lambda p$ describes the plasmon resonance, and $\lambda 0$ is the wavelength in vacuum. The concept of effective wavelength can be also described classically when the resonant structure is between two media, as it happens with the elements considered in this paper. In this case, the effective wavelength is given as Display Formula$\lambda eff=\lambda 0\u03f5SiO2+\u03f502,$(7)
where $\u03f5SiO2$ and $\u03f50$ are the dielectric permittivity of $SiO2$ and vacuum respectively. However, when simulating the response of the device we can parameterize it with respect to the skin depth of the material. The result (see Fig. 3) shows that shorter dipoles are better for a larger skin depth, as expected from previous published results.^{8}^{,}^{11} Because of manufacture tolerances, this effect seems a disadvantage when considering Titanium as a construction material for optical antennas. However, as we will see in the next section, the resonant length and the total response of the device also depends on the antenna thickness, which can be tailored according to the material’s characteristics.