# Wavelength-Dependent Nonlinear Absorption in Palladium Nanoparticles
## 3 Results and Discussion  
The characteristics of the PdNPs are shown in Figure 1. Figure 1a is the photo of the PdNPs, and the incident light illuminating is from the illumination of the lab. The sample is khaki-colored, which results from the selective optical absorption of the sample. Figure 1b is the SEM appearance of PdNPs, which implies the nanoparticle is sphere. The particle diameter is 16 nm \(\pm\) 2 nm. Figure 1c shows the linear absorption spectrum of PdNPs. Obviously, there is an absorption peak at about 286 nm which is due to SPR. The nonlinear absorption characteristics of PdNPs were studied in the wavelength range of 500 nm to 650 nm by using OA Z-scan. Representative experimental results at wavelengths of 500 nm, 550 nm, 600 nm and 650 nm were shown in Figure 2a-d where the normalized transmission changing with the Z position was given under different excitation energies of 630 \(\upmu\)J, 730 \(\upmu\)J and 752 \(\upmu\)J, respectively. The normalized transmission is the measured transmission divided by the linear transmission of 40%. As shown in Figure 2a, when the wavelength of the laser used in the experiment is 500 nm, under three excitation energies (630 \(\upmu\)J, 730 \(\upmu\)J, 752 \(\upmu\)J), the Z-scan traces recorded show an increasing transmission around the focal point (sample position, \(z=0\)), but a dip appears at the focal point. The shape of the Z-scan curve suggests that the sample exhibits the transformation from SA to RSA. With the increase of excitation energy, the peak value of both wings decreases and the bandwidth increases, while the valley becomes deeper and deeper, which indicates that the sample shows stronger RSA at higher laser energy. Figure 2b shows the experimental results obtained at 550 nm laser wavelength, whose curves are basically similar to those in Figure 2a. But the amplitude of peaks and valleys in Figure 2b are smaller than those in Figure 2a. Figure 2c shows that when the wavelength is 600 nm and the excitation energy is weaker (630 \(\upmu\)J, 730 \(\upmu\)J), the sample displays SA. But when the excitation energy increases to 752 \(\upmu\)J, the transmission of the sample increases firstly and then decreases, which means the transformation from SA to RSA. Figure 2d is the experimental result obtained at wavelength of 650 nm. Similarly, when laser energy is weaker (630 \(\upmu\)J, 730 \(\upmu\)J), the sample exhibits SA, but transforms from SA to RSA at higher energy (752 \(\upmu\)J). Relatively, the amplitude of peaks and valleys in Figure 2d are smaller than those in Figure 2c. In order to better understand the results above, the relationship between the normalized transmission of PdNPs and the incident laser pulse energy density was shown in Figure 3a-d.  
Figure 1: Characteristics of PdNPs. (**a**) Photo of the sample. (**b**) SEM image. (**c**) Linear absorption spectrum. From Figure 3a,b, we can found that the transmission of the sample first increases with laser influence, then decreases, which means the transformation from SA to RSA. In  
Figure 3: The relationship curve between the normalized transmission of PdNPs and the incident laser pulse energy density under different wavelengths of (**a**) 500 nm, (**b**) 550 nm, (**c**) 600 nm and (**d**) 650 nm. The dotted lines are experimental data. Figure 2: Normalized transmission of PdNPs for open aperture Z-scan measurement under different wavelengths of (**a**) 500 nm, (**b**) 550 nm, (**c**) 600 nm and (**d**) 650 nm. The dotted lines are experimental data while the solid lines are theoretical fits. Figure 3c,d, when laser energies are 630 \(\upmu\)J, 730 \(\upmu\)J, the normalized transmission increases with laser influence, which means only SA. At 752 \(\upmu\)J, the transmission increases first and then decreases, which implies transformation from SA to RSA.