## 4 OES for the Laser Induced Plasma Investigation  
As mentioned in the previous paragraph, in the case of ns-laser ablation, the source of material for NP generation is the plasma. For this reason, retrieving information on the plasma system is of great importance to understand the PLAL processes. As a consequence of the high ionization degree and the high temperature, the plasma is characterized by an intense emission of light that can be investigated with the optical emission spectroscopy, OES. The instrumental set up for OES is sketched in Figure 2, where the integrated plasma emission intensity is collected on the slit of the spectrometer through a lens and the spectrometer is coupled with an ICCD to obtain the temporal evolution acquisition of the plasma emission. In the case of laser-induced plasma in liquid, the plasma expansion is notably confined, not only for the low compressibility of the liquid phase, but especially because the fast energy transfer from the plasma to the liquid induces the vaporization of the surrounding liquid and the production of a water vapor thin layer [9]. The latter, that is the starting point of the cavitation bubble [13], is characterized by high temperature and high pressure and consequently expands in all directions. Therefore, the high pressure of the cavitation at the early stage of bubble formation contains the plasma and confines it in a small volume. The main effect of this strong confinement is that the matter in the plasma phase holds a high number density for the entire plasma lifetime [9,12]. This phenomenon can be directly appreciated with the spectral features of the plasma emission. The emission spectrum of the laser-induced plasma is characterized by the absence of discrete emission  
Figure 2: Sketch of the experimental set-up for optical emission spectroscopy (OES) of laser-induced plasma in liquid. lines and by a continuum spectrum resembling the Planck-like distribution of photons, as shown in Figure 3a, where a typical example of temporal evolution of the continuum radiation spectra of LIP is shown. The absence of the discrete emission lines that generally characterize laser-induced plasma in a gas and vacuum environment, is related to the high-density effects. According to [PERSON] or [PERSON] theories, the cut-off of the levels occurs when excited levels cannot be achieved as a consequence of a sharp lowering of the ionization energy [13]. This happens because of the high density (10\({}^{20}\)-10\({}^{22}\) cm\({}^{-3}\)) that constrains the excited atom's expansion ([PERSON])--the distance between particles is smaller than the size of the excited particle--or because of the high electron number density (10\({}^{19}\)-10\({}^{21}\) cm\({}^{-3}\)) that affects the Coulomb potential of the particle (Debye\(-\)Huckel effect) [14]. For this condition, the radiative recombination is the main contribution to the spectrum as discussed in Ref. [15]. As a result of this high density effect, the spectral distribution is proportional to the Planck's distribution [15]. In the visible range of the spectrum, the Wien's approximation can be assumed so that [7]:  
\[I(\lambda)=G(T,N_{e})\frac{8\pi hc^{2}}{\lambda 5}\exp\biggl{(}-\frac{hc}{ \lambda kT}\biggr{)}d\lambda \tag{1}\]  
In Equation (1), h is the Planck constant, k the Boltzmann constant, c the speed of the light and G(T, Ne) represents a function depending on detection efficiency, on the electron number density (Ne) and plasma temperature (T), but not on the wavelength. The Planck distribution can be plotted in the logarithmic form to determine the temperature of the plasma from the inverse of the slope as shown in Figure 3b:  
\[\ln\biggl{(}\frac{I_{\lambda}\cdot\lambda^{5}}{8\pi hc^{2}}\biggr{)}=Q-\frac{ hc}{\lambda kT} \tag{2}\]  
Note that the intensity, I\({}_{\lambda}\), used in the Planck plot is integrated over a small wavelength range (e.g., corresponding to the spectral resolution of the detection system).