# Wavelength-Dependent Optical Nonlinear Absorption of Au-Ag Nanoparticles
## 3 Results and Discussions  
In the TEM image shown in Figure 1a the structure composed of an Au core and an Ag shell can be seen clearly, and the Au-Ag NPs have a uniform size distribution. The average diameter of the Au-Ag NPs was around 75 nm, and the Au core radius was about 26.5 nm, with a thickness of about 11 nm for the Ag shell. As shown in the photograph in Figure 1b, the Au-Ag NPs were light brown. This resulted from the selective absorption of incident light by the Au-Ag NPs. Figure 1b displays the linear absorption spectra (red solid line) of the Au-Ag NPs. We can observe an absorption peak at 510 nm, which was from the LSPR of the Au cores. The LSPR was from the collective oscillation of conduction electrons near the Fermi level caused by an electromagnetic field, which strongly depends on composition, shape, and size of materials [41]. The blue line in Figure 1b is the simulated absorption data of a single Au-Ag NP. It can be found that the simulation data was basically similar to the experimental absorption spectra. To verify the origin of the spectra differences, we studied theoretically the effect of the Au core radius and the Ag shell thickness on LSPR absorption spectra of Au-Ag NPs by using FDTD (the absorption mentioned here is truly exclusively the absorption, because it did not include scattering). The simulation absorption spectra are shown in Figure 2.  
Figure 1: Characterization of the Au-Ag NPs. (**a**) TEM image. (**b**) Linear absorption spectra; inset image: photograph of the Au-Ag NPs’ water-soluble dispersion. We can observe from Figure 2a that the absorption peak showed an obvious redshift with an increasing radius of the Au core, when the overall sizes of Au-Ag NPs were unchanged. The change of radius of the Au core caused the absorption peak to shift. With the radius of Au core increasing, the optical properties of Au-Ag NPs were mainly characterized by the LSPR of the Au cores. Figure 2b shows the relationship between the position of the absorption peak and the radius of the Au core; we found that they were approximately linear. After the simulation, we found that the absorption peak position of the Au-Ag NPs was related to the Au core radius and the Ag shell thickness. The Au-Ag NPs we used cannot be synthesized with the same Au core radius and Ag shell thickness, and there must be a certain size distribution, so the simulation absorption spectra were not completely consistent with the experimental ones. The repetition rate of the laser used in the OA Z-scan experiments was 10 Hz, which was low enough to avoid the thermal effect [42; 43]. Previous reports generally focused on the nonlinear characteristics of the materials excited by a single laser wavelength near the resonance absorption peak. To research the nonlinear optical absorption of the samples being excited by different wavelengths, 450 nm, 510 nm, 550 nm, and 600 nm pulsed laser produced by OPO were used. Laser pulse energies of 260 \(\upmu\)J and 760 \(\upmu\)J (intensity I\({}_{0}\) at the focus of 1.04 \(\times\) 10\({}^{13}\) and 3.03 \(\times\) 10\({}^{13}\) W/m\({}^{2}\), respectively) were chosen for the experiments. The normalized OA Z-scan transmittance of the Au-Ag NPs is presented in Figure 3a-d. The transmittance in this experiment was calculated by dividing the energy through the sample by that of the input sample. When the input energy was constant, the light intensity and nonlinear absorption coefficient of the sample at different Z positions was different, which made the energy passing through the sample change. Dividing the output energy of each Z point by the input energy gives the transmittance of that point. For the convenience of calculation and comparison, the normalized transmittance was obtained by dividing the transmittance of each point by the linear transmittance measured at the corresponding wavelength. Figure 3a-d illustrate that, under the excitation energy of 260 \(\upmu\)J, when the sample approached the focal point, the normalized transmittance increased gradually.