Non-linear surface Kerr effect and SHG in magnets

Non-linear surface magneto-optical response of a ferromagnetic metal is considered in the frame of conventional magneto-optic formalism in order to provide a basis for comparing the linear and non-linear magneto-optic effects. Formulae are given for the total linear and non-linear magneto-optical Kerr effect. The odd with respect to the magnetization the variation of the second harmonic generation (SHG) signal of a transmitted light passing through a transversely magnetized ferromagnetic film is studied.