Nonlinear anomalous ferromagnetic Faraday effect.

Abstract

Two electromagnetic waves with the same frequencies and different polarizations may propagate together in a saturated ferrite. We investigate how the simultaneous presence of the two waves affects their modulation. It is found that their evolution is governed by two independent nonlinear Schr\"odinger equations. A phase factor corresponding to a weak interaction is created: it is interpreted as a nonlinear Faraday effect. Then, for high frequencies, we build a perturbative method adapted to the study of the nonlinear Faraday effect. The angle of rotation of the polarization is calculated and expressed in terms of generalized Stokes parameters of the waves. For the linear case, it is well known that the Faraday effect has the following important property: when the wave is reflected back and passes through the sample of ferrite in the opposite direction, the Faraday effect rotates the polarization of the reflected wave in the same way as the incident one; thus the additional rotation angle is added to the first one instead of canceling it. We describe a normal Faraday effect, which has the same property, and an anomalous effect, for which the rotation is canceled in the same conditions. The normal effect is proportional to the energy density of the incident wave, and the anomalous effect to the difference of intensity between the two elliptic polarizations. Finally, we discuss ways of making evident these higher-order effects.