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

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 magento-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 magento-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 4x4 matrix formalism is replaced by a 2x2 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.