Retrieving linear and nonlinear optical dispersions of matter: combined experiment-numerical ellipsometry in Silicon, Gold and Indium Tin Oxide

TL;DR

This paper introduces a combined experimental and theoretical method using a hydrodynamic model to accurately determine the linear and nonlinear optical dispersions of nanostructured materials like silicon, gold, and ITO, especially in complex scattering or absorbing regimes.

Contribution

It develops a practical approach that integrates harmonic generation measurements with a hydrodynamic model to retrieve complex nonlinear dispersion curves for various materials.

Findings

Silicon and gold nonlinear susceptibilities match analytical models.

Predicted chi3 values for silicon in visible and IR ranges.

Estimated nonlinear susceptibilities for ITO and implications for device physics.

Abstract

The predominant methods currently used to determine nonlinear optical constants like the nonlinear refractive index n2 or chi3 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 ps or fs regimes demands the development of new theoretical tools 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 a 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, silicon, gold, and indium tin oxide, 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 based on the nonlinear oscillator model. Based on our assessment of THG conversion efficiencies in silicon, we predict chi3(w) and chi3(3w) are of order 10^(-17)(m/V)^2, in the visible and IR ranges, with respective peaks of 10^(-14) and 10^(-16)(m/V)^2 in the UV range. Similarly, gold's chi3(w) and chi3(3w) are of order 10^(-17) and 10^(-16)(m/V)^2, and predict chi3(w)~10^(-17)(m/V)^2 and chi3(3w)~10^(-18)(m/V)^2 for ITO. These results suggest that judicious exploitation of the nonlinear dispersion of ordinary semiconductors can transform device physics in spectral regions that extend well into the UV range.