Computational Kerr-Ellipsometry: Quantifying Broadband Optical Nonreciprocity of Magneto-Optic Materials

Abstract

Characterizing the optical response of magneto-optic and magnetic materials usually relies on semi-classical models (e.g. Lorentz oscillator model) involving few parameters or models based on a detailed quantum mechanical description of the underlying response. These models typically involve a few parameters that are estimated via fitting the experimental data to provide a qualitative understanding of the underlying physics. Such a few-parameters fitting approach falls short of accurately capturing all elements of the complex-valued permittivity tensor across a range of wavelengths. Accurate characterization of the permittivity tensor elements across a broad range of wavelengths is invariably imperative for designing optical elements such as isolators, circulators, etc. Here, we propose and demonstrate a ubiquitous and accessible method based on a combination of spectroscopic ellipsometry and spectroscopic Magneto-Optic Kerr Effect (MOKE) measurements coupled with rigorous numerical parameter extraction techniques. To this end, we use the combined MOKE ellipsometry measurements conducted at different angles of incidence with a gradient-descent minimization algorithm to provide the inverse solution to the complete dielectric permittivity tensor. Further, we demonstrate model re-verification to ensure the estimated dielectric permittivity values reliably predict the measured experimental data. Our method is a simplified bench-top counterpart to the otherwise complex measurement systems.