Third-order nonlinear refraction in porous silicon: theory versus experiment

A z-scan measurement of the nonlinear refractive index of porous silicon (P S) is performed at a photon energy well below the effective bandgap of the sample. The measure gives Re-chi((3)) approximate to -10(-8) esu, that is f our orders of magnitude larger than the bulk value. We also present a calcu lation of the enhancement of ((3))(chi) in PS due to the spatial quantum co nfinement of the exciton in the quasi-one-dimensional nanostructure. The ca lculated enhancement is in very good agreement with the experimental data. Finally, we performed a perturbative calculation of nonlinear absorption De lta alpha in a quantum wire, obtaining the material-independent dispersive scaling of the quantum wire nonlinear refractive index. The calculation sug gests the presence of a 'quantum-confinement-enhanced' quadratic Stark effe ct in the quasi-one-dimensional structure that gives a low and almost const ant value of Re-chi((3)) at photon energy around half-bandgap and large neg ative values in the range E-gap/2 < (h) over bar omega < E-gap. As we discu ss, this prediction is also in good agreement with the experimental results .