General analytical treatment of optics in layered structures: Application to magneto-optics

Abstract

We have derived compact and interpretable analytical expressions to describe the magneto-optics in layered structures for all orientations of magnetization and incident angle. In our approach, the multilayer system is considered as nonmagnetic and the magneto-optical effect is described by an induced electrical polarization. The electromagnetic waves radiated by this polarization are calculated via a propagative treatment and are also shown to directly derive from the Lorentz reciprocity theorem. The expressions of the magneto-optical components of the fields transmitted and reflected in the external media are easily interpretable. Only three relevant quantities are involved: the exciting field, the magnetization, and an extraction vector. The practical calculation is very simple in the framework of the first Born approximation as the 4\ifmmode\times\else\texttimes\fi{}4 matrix formalism is replaced by a 2\ifmmode\times\else\texttimes\fi{}2 matrix resolution. The whole approach is not restricted to magneto-optics and the case of a variety of other systems exhibiting weak induced polarizations originating from anisotropy, bianisotropy, nonlinearity, or inhomogeneity is treated. Higher-order approximations are also discussed and an analytical approximation for large induced polarizations in thin layers is derived.