# Optimization of Nonspherical Gold Nanoparticles for Photothermal Therapy
## 3 Results and Discussion
To investigate the effect of the excitation wavelength on the optimization results, wavelengths from 800 to 1100 nm were selected because they are the main wavelength range for lasers used in PTT. The optimization results for the three types of gold nanoparticles at the wavelength range between 800 and 1100 nm are shown in Figure 3. Due to the increase of the excitation wavelength, the light absorption ability of each nanoparticle becomes higher (Figure 3a), the optimal aspect ratios of nanoparticles increase almost linearly (Figure 3b), and the optimal lengths of nanoparticles increase in a stepwise manner (Figure 3c). The optimized nanospheroids exhibited the highest light absorption ability at all wavelengths, while the optimized nanocylinders showed a slightly higher light absorption ability than that of the optimized nanorods. Both the optimal aspect ratio and the length of a nanospheroid were larger than those of a nanocylinder and nanorod, while the optimized nanocylinder displayed smaller size parameters than that of the optimized nanorod. Due to the increase in the wavelength from 800 to 1100 nm, the maximum volume absorption coefficient of the nanospheroid increased from 348.7 to 450.3 \(\upmu\)m\({}^{-1}\), the optimal aspect ratio of the nanospheroid increased from 3.7 to 6.2, and its optimal length exhibited an increase from 59 to 100 nm. The refractive index of the surrounding medium is an important parameter impacting the light absorption property of gold nanoparticles. In the calculations performed in this study, the surrounding medium was considered to be biological tissue with a refractive index between 1.35 and 1.7 [22]. Figure 4 demonstrates the effect of the refractive index of tissue on the optimization results. Due to the increase of the refractive index of tissue, the light absorption ability of each nanoparticle decreases almost linearly (Figure 4a), and the optimal size parameters of the nanoparticles become smaller (Figure 4b,c). Clearly, the change of the refractive index of tissue does not make the light absorption ability of a nanospheroid lose its dominant position. Both the optimal aspect ratio and the length of a nanocylinder are smaller than those of a nanospheroid and a nanorod. An optimized nanospheroid has larger size parameters than an optimized nanorod. With the increase in the refractive index from 1.35 to 1.7, the maximum volume absorption coefficient of a nanospheroid decreases from 369.8 to \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{_A (nm)_} & \multicolumn{2}{c}{\(\boldsymbol{\alpha_{\text{abs,max}}}\) (\(\upmu\)m\({}^{-1}\))} & \multirow{2}{*}{\(\boldsymbol{\alpha_{\text{abs,max}}^{nanospheroid}}/\boldsymbol{\alpha_{\text{abs,max}}^{nanoshell}}\)} \\ \cline{2-3}  & **Nanospheroid** & & \\ \hline
800 & 348.7 & 117.4 & 3.0 \\
808 & 352.1 & 114.9 & 3.1 \\
820 & 359.0 & 111.4 & 3.2 \\
1064 & 442.0 & 62.5 & 7.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Maximum volume absorption coefficients \(\alpha_{\text{abs,max}}\) of gold nanospheroids and nanoshells (hollow core) at four typical excitation wavelengths (800, 808, 820, and 1064 nm). The refractive index of tissue is 1.44. Figure 3: (**a**) Maximum volume absorption coefficient \(\alpha_{\text{abs,max}}\), (**b**) optimal aspect ratio \(R_{opt}\), and (**c**) optimal length \(L_{opt}\) of gold nanospheroid, nanocylinder, and nanorod at excitation wavelengths from 800 to 1100 nm at a step size of 10 nm. The refractive index of tissue is 1.44. 305.2 \(\upmu\)m\({}^{-1}\), the optimal aspect ratio of a nanospheroid decreases from 4 to 2.9, and its optimal length decreases from 69 to 49 nm. The above-mentioned discussion clearly indicates the presence of only one group of optimized size parameters for a fixed excitation wavelength and a known biological tissue. However, it is difficult to prepare the gold nanoparticles of the same size in the actual particle synthesis as the optimized results.