Magneto-optical Kramers-Kronig analysis

Abstract

We describe a simple magneto-optical experiment and introduce a magneto-optical KramersKronig analysis (MOKKA) that together allow extracting the complex dielectric function for leftand right-handed circular polarizations in a broad range of frequencies without actually generating circularly polarized light. The experiment consists of measuring reflectivity and Kerr rotation, or alternatively transmission and Faraday rotation, at normal incidence using only standard broadband polarizers without retarders or quarter-wave plates. In a common case, where the magneto-optical rotation is small (below ∼ 0.2 rad), a fast measurement protocol can be realized, where the polarizers are fixed at 45 • with respect to each other. Apart from the time-effectiveness, the advantage of this protocol is that it can be implemented at ultra-high magnetic fields and in other situations, where an in-situ polarizer rotation is difficult. Overall, the proposed technique can be regarded as a magnetooptical generalization of the conventional Kramers-Kronig analysis of reflectivity on bulk samples and the Kramers-Kronig constrained variational analysis of more complex types of spectral data. We demonstrate the application of this method to the textbook semimetals bismuth and graphite and also use it to obtain handedness-resolved magneto-absorption spectra of graphene on SiC.

Colossal infrared and terahertz magneto-optical activity in a two-dimensional Dirac material

“…By combining the Faraday-rotation and magneto-transmission spectra, we can extract the absorption for the RHC and LHC polarizations 14,21 (Figs. 4f − 4i)).…”

Fanoq-reversal in topological insulator Bi2Se3

“…In addition, we also detect relatively large changes in the very far-infrared part of the spectrum, around 60 cm −1 phonon mode. Kramers-Kronig transformation is not directly applicable to magneto-optical spectra [19], so instead we apply the fitting procedures, and from the best fits we generate the optical functions of interest. The most frequently used model is the Drude-Lorentz model, supplemented with the cyclotron resonance [20].…”

Spectral curve fitting of dielectric constants

“…7,17,27 Note that a triangular shape is B-spline of degree one but B-splines of various degrees can also be employed. 17 The idea is to find a set of triangular basis functionsε j (v) anchored at ν j so that the imaginary part of the dielectric constant can be expressed as a linear combination of these basis functions.…”

“…As an intrinsic property of the material, 1 optical constants contain information on the composition of material, 2-4 its anisotropy, [5][6][7] and its optical activity. 8 The optical properties of a material can be inferred from experimental spectra from X-ray frequencies through to the Far-Infrared/Terahertz regions, in either transmittance or absorbance or reflectance mode.…”

“…A more versatile but less physically intuitive way to model optical constants is to use K-K consistent functions which are capable of fitting various line shapes. 7,17,22,25,[27][28][29][30] However, there is no comparison of these methods in a systematic and comprehensive manner. The purpose of this manuscript is to scrutinize four commonly employed line shape functions using representative…”