Retrieving Linear and Nonlinear Optical Dispersions of Matter: Combined Experiment-Numerical Ellipsometry in Silicon, Gold and Indium Tin Oxide

Abstract

The predominant methods currently used to determine nonlinear optical constants like the nonlinear refractive index n2 or the third order susceptibility χ(3) rely mostly on experimental, open and closed z-scan techniques and beam deflection methods. While these methods work well when the linear absorption is relatively small or negligible, the retrieval process is more complicated for a strongly scattering, dispersive or absorbing medium. The study of optics at the nanoscale in the picosecond or femtosecond laser pulsed regimes demands the development of new theoretical tools, and diverse experimental approaches, to extract and verify both linear and nonlinear optical dispersions exhibited by matter, especially when material constituents are fashioned into nanostructures of arbitrary shape. We present a practical, combined experimental and theoretical approach based on the hydrodynamic model that uses experimental results of harmonic generation conversion efficiencies to retrieve complex, nonlinear dispersion curves, not necessarily only for third order processes. We provide examples for materials that are of special interest to nanophotonics, for example, silicon, gold, and indium tin oxide (ITO), which displays nonlocal effects and a zero-crossing of the real part of the dielectric constant. The results for silicon and gold compare well with analytical predictions of nonlinear dispersion based on the nonlinear oscillator model. Based on our assessment of third harmonic generation conversion efficiencies in silicon, we predict χω(3) and χ3ω(3) are of order 10−17 (m/V)2 in the visible and near IR ranges, with respective peaks of 10−14 (m/V)2 and 10−16 (m/V)2 in the UV range. Similarly, gold’s χω(3) and χ3ω(3) are of order 10−17–10−16 (m/V)2, and predict χω(3)∼10−17(m/V)2 and χ3ω(3)∼10−18(m/V)2 for ITO. These results clearly suggest that judicious exploitation of the nonlinear dispersion of ordinary semiconductors has the potential to transform device physics in spectral regions that extend well into the UV range.