<title>Linear and quadratic magneto-optical effects in reflection from a medium with an arbitrary direction of magnetization</title>

Abstract

Three basic configurations are usually distinguished in calculations of the light propagation in magneto-optical media: polar, longitudinal and transverse direction of the magnetization. In these particular cases the fourth order equations for normal components of the wave vectors reduce to bi-quadratic ones. Analytic solutions of this equation are obtained also for a mixture of longitudinal and transverse effects (magnetization in the plane of interface) and for a mixture of polar and transverse effects. These configurations are discussed in details. If the magnetization is in general direction, the fourth-order characteristic equation has to be solved by using numerical methods. Permittivity tensor is considered for the case of cubic magneto-optical crystal. Its linear and quadratic terms in magnetization are included. The magneto-optical medium is described by the index of refraction and by linear and quadratic epitaxial Fe layer on MgO substrate. The magnetization component effects in general direction are studied by numeric calculations of the reflection coefficients. The mixture of the polar, longitudinal and transverse magneto-optical effects is analyzed taking into account the second order terms. The effects of the magnetization components are specified at normal incidence geometry, because in this case the calculation becomes simpler.