Effective nonlinear refractive index of nano-porous silicon and its dependence on porosity and light wavelength

In this paper, we study the dependence of effective optical linear and nonlinear refractive indices of nano-porous silicon layers on crystalline silicon substrates on fill fraction, at different light wavelengths in visible and near-infrared. Simple approximative formulae, in the frame of Bruggeman's formalism, that describe the dependences of effective optical linear and nonlinear refractive indices of nano-porous silicon on fill fractions and on wavelength, in the range of 620 - 1000 nm, are derived. Experimental results with reflection intensity scan show a good agreement with the data provided by our formulae and the exact results of Boyd-Bruggeman's formalism for the third order nonlinearity, in the case nanoporous silicon with different porosity and at light wavelengths in the mentioned spectral range.