Effective third-order optical nonlinearity of nano-porous silicon

We study the effective optical linear refractive index and the effective optical third-order nonlinear susceptibility of nano-porous silicon layers on crystalline silicon substrate, in function of fill fraction and light wavelength. Starting from Bruggeman's effective medium theory and Sellmeier's dispersion formalism (for silicon), we derive simplified approximative formulae that describe the dependences of effective optical linear and third-order nonlinear properties on both fill fraction and wavelength, in the spectral range covering visible and near-infrared. The experimental data obtained from reflectivity measurement (in the case of effective linear refractive index) and by reflection intensity scan (in the case of effective third-order nonlinearity) are in good agreement with the data predicted by our approximative formulae and with the results of Bruggeman's effective medium theory, for nano-porous silicon.