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Magneto-optical normal incidence polar Kerr effect of inhomogeneous multilayers

The normal incidence magneto-optical (MO) polar Kerr effect is considered on the basis of an idealized phenomenological model of plane wave reflection from inhomogeneous multilayers. They may be periodic or non-periodic, and each layer may have any thickness and constant refractive index, with the small MO Q-parameter being an arbitrary function of the coordinate along the direction of wave propagation. A new algorithm, involving a regular perturbation method for solving the wave equation, to find the state of polarization (Kerr angle and ellipticity) and amplitude reflectance is comprehensively outlined and shown to be conveniently used in terms of the characteristic matrix technique as well as being free from any numerical disadvantages. A few model distributions of the inhomogeneity are used to illustrate its influence on the Kerr effect. An exact analytical solution, found for a semi-infinite MO medium with Q-parameter (not necessarily small) as an exponential function, is given to confirm the validity and good accuracy of the results produced by means of the general approach.