CORRECT FORMULATION OF 1ST-ORDER MAGNETOOPTICAL EFFECTS IN MULTILAYER THIN-FILMS IN TERMS OF CHARACTERISTIC MATRICES AND DERIVATION OF A RELATED SUPERPOSITION PRINCIPLE

The correct formulation of first-order magneto-optical effects in magnetic multilayer systems is discussed in terms of the 4 x 4 characteristic matrix method applied to the polar, longitudinal and transverse orientations. It is emphasised that the current practice of describing the behaviour of multilayered media by forming the iterated product of the matrices of the individual layers does not lead to self-consistent results unless terms of order greater than unity in the magneto-optic parameter are always neglected. A procedure for dealing with multilayered magnetic media, which is entirely self-consistent, is described in terms of a consideration of the 2 x 2 matrix components of the general 4 x 4 characteristic matrix. In the development of the basic formalism for dealing correctly with first-order magneto-optic effects it has also been possible to demonstrate that a superposition principle generally holds true. According to this principle, the magneto-optically induced electric field components resulting from an interaction of electromagnetic radiation with a magnetic multilayered system are linear superpositions of the complex magneto-optic fields due to individual magnetic elements in the system, where the fields associated with each element are calculated on the basis that the rest of the system is non-magnetic.