# Femtosecond Optical Nonlinearity of Nanodiamond Suspensions
## 2 Materials and Methods
The measured Raman spectra of detonation and HP-HT nanodiamond films show pronounced peaks with frequency shifts of 1329 and 1330 cm\({}^{-1}\), respectively (see Figure 2a). Taking into account the known dependences of the Raman shifts of carbon nanomaterials on the excitation wavelength [53] and the nanoparticle size [54], one can attribute these peaks to nanodiamonds (sp\({}^{3}\)-form of carbon). The decomposition of the spectra presented in Figure 2a shows that the full width at half maximum (FWHM) of diamond lines of HP-HT and detonation nanodiamonds are 8 and 22 cm\({}^{-1}\), respectively. It is noteworthy that along with the specified peaks, the Raman spectra exhibit broad luminescence bands caused by defects of various natures contained in HP-HT and detonation nanodiamonds [29; 55]. For the X-ray diffraction studies, nanodiamond powders were obtained by drying the suspensions at room temperature and subsequent mechanical grinding. When obtaining diffraction patterns, the studied powders were placed on a glass substrate. The diffraction pattern of the substrate without powder was recorded separately. To obtain the diffraction pattern of the studied powder, the corresponding subtraction of the substrate response from the experimental data was performed. The crystalline structure of the nanodiamonds was studied using Bruker D2 PHASER X-ray diffractometer with a copper-based X-ray tube generating radiation at a wavelength of 0.1541 nm (K\({}_{\alpha 1}\) line). The diffraction patterns of the detonation and HP-HT nanodiamonds powders (see Figure 2b) contain three solitary peaks in the range of 26 variation from 25\({}^{\circ}\) to 100\({}^{\circ}\). These peaks are observed at 20 angles of 43.9\({}^{\circ}\), 75.3\({}^{\circ}\), and 91.5\({}^{\circ}\). They correspond to X-ray diffraction on the (111), (220), (311) planes of diamond crystallites with interplanar spacings of d\({}_{111}\) = 0.2060 nm, d\({}_{220}\) = 0.1261 nm, and d\({}_{311}\) = 0.1075 nm, respectively, where the subscripts at d denote crystallographic planes. Note that according to the reference data of diamond (see Figure 2b), the intensities of the diffraction lines of monochromatic radiation on the (111), (220), (311) planes are equal to 100, 25, and 16 arb. units, respectively (see Powder Diffraction File (PDF) 00-006-0675). Figure 2b shows that for both diffraction patterns, the ratio between peak amplitudes at angles 20 equal to 43.9\({}^{\circ}\), 75.3\({}^{\circ}\), and 91.5\({}^{\circ}\) is the same. Processing the measured X-ray diffraction pattern using TOPAS 4.2 software revealed that the mean crystallite sizes (LVol-IB) of the HP-HT and detonation nanodiamond particles are 8.6 and 2.7 nm, respectively. Thus, the  
Figure 2: (**a**) Raman spectra of HP-HT and detonation nanodiamonds film and (**b**) X-ray diffraction patterns of HP-HT and detonation nanodiamond powders. The X-ray diffraction pattern of diamond (Powder Diffraction File 00-006-0675) is presented for a reference. measurements on an X-ray diffractometer show that all the samples under study consist of diamond material. For the optical measurements, suspensions of both types of nanodiamonds were prepared at three concentrations. Figure 3 shows the optical densities of aqueous suspensions of HP-HT and detonation nanodiamonds at three different concentrations measured in a 1 mm thick optical quartz cell. The measurements were performed using a PerkinElmer Lambda 650 (Shelton, WA, USA) two-beam spectrophotometer relative to the same 1 mm-thick quartz cell filled with distilled water. It can be seen that for the suspensions of both types of nanodiamonds, the optical density decreases monotonically with an increase of light wavelength which is the characteristic of nanodiamonds [29; 32; 49; 56; 57]. For the suspensions of HP-HT nanodiamonds, the increase in optical density with decreasing wavelength is more pronounced than for the suspensions of detonation nanodiamonds.