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.