## 3 Discussion  
The porous silicon used in this work consists of quasi-one-dimensional wires with a mean diameter of 10 nm. Therefore, the motion of the charged carriers is moderately confined. As a result of the confinement effect, the optical matrix element, defining the third order-nonlinear susceptibility (\(\chi^{3}\)), increases. [PERSON] et al. [25] proposed a computational model to calculate \(\chi^{3}\) as a function of quantum wire radius. It was suggested that for a quantum wire with a 2-3.5-nm radius, the real part of \(\chi^{3}\) is about four orders of magnitude greater than in the bulk. From our experimental results, we obtained \(\Re(\chi^{3})=\frac{4}{3}n_{2}n_{0}^{2}e_{0}c=1.2\times 10^{-19}\) m\({}^{2}\)/V\({}^{2}\) for \(p\)-Si, which is an order of magnitude greater than \(3.37\times 10^{-20}\) m\({}^{2}\)/V\({}^{2}\) for \(c\)-Si. The difference of our result as compared to [PERSON]'s work might be the weaker confinement in our samples.  
Moreover, in addition to the confinement, the optical Stark effect plays an important role in low-dimensional systems and can cause the sign reversal of \(n_{2}\) (proportional to \(\Re(\chi^{3})\)) in \(p\)-Si. To demonstrate this effect, [PERSON] et al. employed the sum-over-states method for the calculation of \(\chi^{3}\) of a sphere in a quantum confinement regime as a function of the sphere radius [14]. The results demonstrated that \(\Re(\chi^{3})\) is always negative with positive values of \(\Im(\chi^{3})\). This behaviour is different from the bulk materials, which exhibit negative values \(\Re(\chi^{3})\) only for photon frequencies very close to the absorption edge.  
Our experimental results also show a suppression of the TPA process for an 800-nm photon wavelength and smaller \(\beta\) in \(p\)-Si with respect to \(c\)-Si. However, it should be noted that the TPA coefficient we evaluated in this work is an effective value of \(p\)-Si. Due to the dilution of silicon with air, the effective \(\beta\) is smaller than that of the silicon constituent, despite possible enhancement by the quantum confinement effect.  
In summary, \(p\)-Si is a nonlinear material where the nonlinear refraction is greatly enhanced, but the nonlinear absorption is slightly suppressed with respect to its bulk counterpart. Such combinations of the coefficients make \(p\)-Si a suitable material for all-optical switching. The requirement for all optical switching is \(\left|\frac{n_{2}}{\beta\lambda}\right|>c_{sw}\), where \(\lambda\) is the wavelength and \(c_{sw}\) is a switching parameter [26], the value of which depends on a particular switching scheme. For example, for a nonlinear coupled waveguide, \(c_{sw}=2\). Our results suggest that for 800-nm \(p\)-Si and \(c\)-Si, \(\left|\frac{n_{2}}{\beta\lambda}\right|=1.19\) and 0.03, respectively. However, at 2.4 \(\upmu\)m, \(p\)-Si gives a promising value for all-optical switching application since \(\left|\frac{n_{2}}{\beta\lambda}\right|=292\). In comparison to other semiconductor composites that have been proposed for all-optical switching (for example Al-Ga-As [27], Ge-As-Se and Ge-As-S-Se demonstrated \(\left|\frac{n_{2}}{\beta\lambda}\right|>5\)[28]), \(p\)-Si has the advantage of the established fabrication technology, relatively low cost and less contamination to the environment.