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

A z-scan measurement of the nonlinear refractive index of porous silicon (PS) 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 four orders of magnitude larger than the bulk value. We also present a calculation of the enhancement of ((3))(chi) in PS due to the spatial quantum confinement of the exciton in the quasi-one-dimensional nanostructure. The calculated enhancement is in very good agreement with the experimental data. Finally, we performed a perturbative calculation of nonlinear absorption Delta alpha in a quantum wire, obtaining the material-independent dispersive scaling of the quantum wire nonlinear refractive index. The calculation suggests the presence of a 'quantum-confinement-enhanced' quadratic Stark effect in the quasi-one-dimensional structure that gives a low and almost constant value of Re-chi((3)) at photon energy around half-bandgap and large negative values in the range E-gap/2 < (h) over bar omega < E-gap. As we discuss, this prediction is also in good agreement with the experimental results.