## 5 Tailoring the Sensitivity of LSPR-Based Sensors Using Simulation Models
### Sensitivity of a Spheroid Au Nanoparticle Embedded in TiO\({}_{2}\)  
In the first set of simulations (Figure 20), the RIS of nanoparticles with different aspect ratios was estimated. In the DDA simulations, the nanoparticles had an effective radius of 8 nm, which represents the radius of a sphere having a volume equal to that of the nanoparticle [229]. The principal settings used in the simulations follow:  
1. Unpolarized light;
2. Four dipoles per nm;
3. Au dielectric function from [PERSON] and [PERSON] [230];
4. TiO\({}_{2}\) dielectric constant (\(\varepsilon=6.8121\), or \(n_{s}=2.61\));
5. Surrounding external refractive index set either to 1.0, 1.3, or 1.5, as a \"semi-infinite\" layer;
6. A wavelength range from 450 to 900 nm with a 5 nm step. Figure 20: Optical extinction efficiency coefficient of spheroidal Au nanoparticles with similar volumes and different aspect ratio (**a**) AR = 1, (**b**) AR = 2, (**c**) AR = 3, and (**d**) AR = 4, and different surrounding refractive indices (\(n_{s}\) = 1.0, 1.3, and 1.5). (**e**) Plot of wavelenght shift (\(\Delta\lambda\)) against \(\Delta n_{s}\) using data taken from (**a**–**d**), and linear fit for each nanoparticle shape to estimate the RIS using the slope. Simulated using nanoDDSCAT+ tool [213]. Considering the size of the nanoparticles used for the simulations, the scattering efficiency coefficient is negligible when compared to the absorption efficiency coefficient (up to three orders of magnitude) [229; 231]. Thus, the extinction efficiency coefficient (the sum of the two previous) presented in the results is roughly the same as the absorption efficiency coefficient. Indeed, it is obvious from Figure 20a-d, that for spheroids with higher AR when the surrounding refractive index increases (from 1.0 to 1.5), the shift of the extinction efficiency coefficient is also increasing from 26 nm for AR = 1 and up to 207 nm for AR = 4. Then, by plotting \(\Delta\lambda\) against \(\Delta n_{s}\) (Figure 20e), the RIS can be estimated: 52 nm/RIU, 158 nm/RIU, 305 nm/RIU, and 414 nm/RIU, for AR of 1, 2, 3, and 4, respectively, thus giving an overall eight-fold improvement. These results are in line with the literature data collection depicted in Figure 18b. From these simulations it looks obvious that the enhanced sensitivity comes from the longitudinal vibration modes of the LSPs, since their intensity seems to be much higher than that of the transverse modes [232]. Therefore, it is advantageous to have nanoparticles with higher aspect ratio since their sensitivity is much higher than spherical shapes. This property might be fine-tuned with the GLAD technique [97]. In the second set of simulations (Figure 21), the effect of a TiO\({}_{2}\) cap layer covering an Au sphere (AR = 1, Figure 21a), an oblate spheroid (AR = 2, Figure 21b), and a prolate spheroid (AR = 2, Figure 21c) were studied. From Figure 21d-f, it can be concluded that by adding a 4 nm and then an 8 nm TiO\({}_{2}\) layer, the intensity of the extinction efficiency coefficient is gradually diminished. Similarly, the sensitivity (RIS) estimated with the against \(\Delta n_{s}\) plots in Figure 21g-i, also decreases with increasing thickness of the surrounding TiO\({}_{2}\) layer. It means that when the Au nanoparticles are grown within an oxide matrix, the sensitivity of the optical LSPR response of the Au nanoparticles is impaired. This effect is due to the plasmon decay length that follows an exponential decrease from the surface of the nanoparticle, as mentioned before. To overcome this hurdle, the surface of the films can be etched to eliminate superficial oxide layers, thus diminishing the distance between the nanoparticles and the molecules to detect, thereby improving the sensitivity. Furthermore, in agreement with the previous set of simulations, the aspect ratio of the nanoparticles also plays an important role when the nanoparticles are covered by the dielectric matrix.