Generalized analytic formulae for magneto-optical Kerr effects

We have developed simplified analytic expressions for magneto-optical Kerr effects of both optically thick and ultrathin films in the general case, where a magnetic medium had an arbitrary direction of magnetization and a beam of light was obliquely incident to the medium. It was found that the simplified analytic formulae for the Kerr effects of p and s waves consisted of a product of two factors for both optically thick and ultrathin films: the prefactor dependent only on the optical parameters of the system and the main factor of the polar Kerr effect for a normal incidence case. We have also derived some useful relations among the Kerr effects in the polar and longitudinal configurations. We have demonstrated that the theoretical calculations using the present analytic formulae could well match the experimental polar and longitudinal Kerr rotation angles of magnetic films measured with varying incident angles.