Retrieving linear and nonlinear optical dispersions of matter: Numerical ellipsometry of silicon and indium tin oxide nanolayers

Methods currently used to determine nonlinear optical constants like n2 or chi3 rely on open and closed z-scan techniques. The study of optics at the nanoscale in the femtosecond regime requires new tools and approaches to extract linear and nonlinear dispersions exhibited by matter. We present a practical approach that amounts to numerical ellipsometry that utilizes experimental harmonic generation conversion efficiencies to retrieve complex, nonlinear dispersion curves. We provide examples of retrieved linear and nonlinear dispersions for a variety of materials, and show that for Silicon the numerical retrieval method yields chi3~10^(-16) (m/V)^2 and chi33w~10^(-17) (m/V)^2 , and visible and near IR ranges. Similarly, we predict chi3~10^(-17) (m/V)^2 and chi33w~10^(-19) (m/V)^2 for ITO as it exhibits linear and nonlinear anisotropic responses due to nonlocal effects.