Quantitative magneto-optical imaging with ferrite garnets

Abstract

Magneto-optical imaging is a powerful technique for studying qualitative features of magnetic flux distributions in superconductors and other magnetic samples. However, magneto-optical imaging does not automatically return two-dimensional maps with the actual values of the magnetic field, due to the non-linear response functions of magneto-optical indicator films and in practice also non-uniform illumination. A quantitative treatment is needed in order to achieve such a calibration. After calibration, one can proceed to deduce the corresponding two-dimensional maps of the current density distribution from inversion of the Biot-Savart law. While there has been published a large amount of work on quantitative magneto-optical imaging, the material is scattered and notation differs significantly between different authors. These notes originate from parts of the Ph. D. thesis of the author and collect the most important materials into a unified and updated treatment. Basic aspects of magnetic flux penetration in superconductors including the Bean model are reviewed briefly in chapter 1. In chapter 2, the method of magneto-optical imaging using the Faraday effect is introduced, together with practical aspects of magneto-optical experiments at low temperatures and the semi-qualitative technique of RGB addition for checking the reproducibility of flux patterns. The physics of magneto-optical indicator films and calibration of magneto-optical images into maps of magnetic field values are discussed in chapter 3. Next, in chapter 4 the Biot-Savart law and fast Fourier transformations are discussed before proceeding to inversion of magnetic field maps into current density maps. Finally, magnetometry with Faraday magneto-optical imaging is treated. MATLAB codes for several of the discussed concepts can be found at https://github.com/atlejq/Magneto-optics