# Femtosecond Optical Nonlinearity of Nanodiamond Suspensions
## 2 Materials and Methods
This can be explained by stronger light scattering in the suspension of HP-HT nanodiamonds caused by the following reasons: (i) the slightly larger average nanoparticle size of the HP-HT nanodiamond suspension compared to the average nanoparticle size of the detonation nanodiamond suspension; (ii) the larger \"effective\" refractive index of HP-HT nanodiamonds compared to the \"effective\" refractive index of detonation nanodiamonds due to the difference in their crystal structures. For both types of nanodiamonds the optical density measured at different wavelengths is proportional to the concentration (see insets in Figure 3a,b). Studies of the nonlinear optical properties of nanodiamond suspensions were carried out using the z-scan technique [58] with femtosecond linearly polarized laser pump (wavelength 795 nm, pulse duration 120 fs, and the repetition rate of 1 kHz). In the experiments, simultaneous measurements of transmittance in the closed- and open-aperture configurations were performed (Figure 4). The laser radiation was focused on a cell with a focal length of 75 mm. The cell had 1 mm-thick quartz walls with a 1 mm opening distance. The laser beam waist radius was w\({}_{0}\) = 12.9 \(\upmu\)m, which corresponds to the Rayleigh length of z\({}_{0}\) = 0.65 mm (z\({}_{0}\)=\(\pi\)w\({}_{0}\)\({}^{2}/\lambda\), where \(\lambda\) is the wavelength). The scanning of the cell was performed along the optical z-axis of the focused laser beam using computer numerical control with a step of 0.1 mm with multiple averaging of the pulse energies E\({}_{\text{oa}}\) and E\({}_{\text{ca}}\) recorded using \"open-aperture\" and \"closed-aperture\" photodetectors, respectively (see Figure 4). Figure 3: The optical density of the (**a**) HP-HT and (**b**) detonation nanodiamond suspensions in 1 mm thick quartz cell. Insets show the corresponding optical density as a function of concentration measured at three different wavelengths of 400, 532, and 795 nm. In the experiments, the dependences of the nonlinear transmittance coefficients T\({}_{\rm{oa,n}}\)(z) = E\({}_{\rm{oa}}\)(z)/E\({}_{\rm{in}}\) (with an open-aperture) and T\({}_{\rm{ca}}\)(z) = E\({}_{\rm{ca}}\)(z)/E\({}_{\rm{in}}\) (with a closed-aperture) were measured during scanning of the cell along the z-axis, where E\({}_{\rm{in}}\) is the incident laser pulse energy measured using a reference photodetector. This made it possible to determine the dependences of the normalized nonlinear transmittance coefficients T\({}_{\rm{oa,n}}\)(z) = T\({}_{\rm{oa}}\)(z)/T\({}_{\rm{oa}}\)(z = \(\infty\)) and T\({}_{\rm{ca,n}}\)(z) = T\({}_{\rm{ca}}\)(z)/T\({}_{\rm{ca}}\)(z = \(\infty\)) with open- and closed-apertures respectively, where T\({}_{\rm{oa}}\)(z = \(\infty\)) and T\({}_{\rm{ca}}\)(z = \(\infty\)) are the optical transmittance coefficients at open- and closed-apertures, respectively, obtained far from the beam waist, i.e., far from z = 0. The energy of laser pulses incident on the cell was varied using a polarizer and a half-wave plate. To visualize nonlinear refraction in the experiments, the ratio of nonlinear transmittance obtained in a closed- aperture to the data obtained in an open-aperture t\({}_{\rm{nr}}\)(z) = T\({}_{\rm{ca,n}}\) (z)/T\({}_{\rm{oa,n}}\) (z) was determined [59].