## 2 Results
Further use of the Maxwell-Garnett model for the \(p\)-Si provided the value of the dielectric function of \(\epsilon_{p-Si}=3.55+0.009i\). The corresponding absorption coefficient, \(\alpha\), was 1.54 cm\({}^{-1}\) at 2.4 \(\upmu\)m. We note that the dopant-induced free carrier absorption was about two orders of magnitude lower than the intrinsic absorption of silicon at 800 nm. Therefore, it could be safely discarded in the calculations for an 800-nm wavelength. Figure 1a,b shows the measurements taken with the closed and open aperture, respectively, of \(Z\)-scan transmittance of the 9 \(\upmu\)m-thick \(c\)-Si thin film, using incident fluences of 40, 54, 68 and 82 nJ. The experimental results were fitted with Equations (1) and (2) to extract the TPA coefficient, \(\beta\), and nonlinear refractive index, \(n_{2}\). The fitting results suggest that \(\beta=2.9\pm 0.9\) cm/GW, while \(n_{2}=7\pm 2\times 10^{-6}\) cm\({}^{2}\)/GW, which are comparable to those previously published elsewhere [16; 17]. The main reason for the observed uncertainties was due to the experimental error of the beam fluence determination. The fluence of the incident light did not exceed the nano-Joule range, and it was difficult to measure its exact value. The error involved in the measurements of the fluence was up to 30%. However, this should not lead to a severe numerical error and deviation from the acceptable standards for these types of experiments. The experimental procedure was repeated to measure the non-linear response of a 15 \(\upmu\)m-thick free-standing \(p\)-Si thin film, and the results are shown in Figure 2. We note, the incident fluence covered a slightly different range than that used for the \(c\)-Si's measurements. This was due to the difficulties in controlling the fluence level in such a low pulse energy range. The analysis revealed the TPA coefficient \(\beta=1.0\pm 0.3\) cm/GW and nonlinear refractive index \(n_{2}=-9\pm 3\times 10^{-5}\) cm\({}^{2}\)/GW. In comparison with that of \(c\)-Si, the TPA appeared to be slightly suppressed. However, the nonlinear refraction was greatly enhanced. Remarkably, the sign of \(n_{2}\) was reversed to the negative in comparison to the positive value of \(c\)-Si. These findings agree with [PERSON]'s work [25] on \(p\)-Si, despite the fact that we used samples with different doping and porosity. To further compare the nonlinear refraction process between _c_-Si and _p_-Si, the nonlinear phase shift \(\Delta\Phi\) for different incident fluences is plotted in Figure 3. The squares represent the experimental values \(\Delta\Phi=\Delta T_{peak-valley}\), and the solid lines are calculated from Equation (3) with the values of \(n_{2}\) obtained from the Z-scan measurements. It can be seen that the phase shift for _p_-Si was at least four-times higher and changed faster as a function of the fluence than that of the _c_-Si, which further confirmed the enhancement of the nonlinear refraction. Figure 1: The experimental (dots) and fitting (solid lines) results of the Z-scan measurements for the 9 \(\upmu\)m-thick-_c_-Si sample at 800 nm, using incident fluence of 40 (magenta), 54 (blue), 68 (green) and 82 nJ (red), respectively. (**a**) Closed aperture Z-scan (normalised transmittance with a 500-\(\upmu\)m aperture). (**b**) Open aperture Z-scan (normalised transmittance without aperture). Figure 2: The experimental (dots) and fitting (solid lines) results of the Z-scan measurements for the 15 \(\upmu\)m-thick _p_-Si sample at 800 nm, using incident fluence of 50 (magenta), 55 (blue), 62.5 (green) and 67.5 nJ (red), respectively. (**a**) Closed aperture Z-scan (normalised transmittance with a 500-\(\upmu\)m aperture). (**b**) Open aperture Z-scan (normalised transmittance without aperture). To further extend our knowledge about _p_-Si nonlinearity, we performed the experiments in the Short Wavelength Infrared (SWIR) where the photon energy is lower than the band-gap.