Faraday rotation of nonlinear long electromagnetic waves in a dielectric medium

By the reductive perturbation method, Faraday rotation of electromagnetic waves propagating in a nonlinear dielectric medium parallel to an external magnetic field is investigated. The derived equation takes the form of derivative nonlinear Schrodinger (DNLS) equation appropriate to boundary value problems. Based upon this equation, we have considered how the linear Faraday effect is modified. It is found that a linearly polarized wave incident to the dielectric medium under an external magnetic field shows the Faraday rotation whose angle is the same as that for linear waves in the lowest order but slightly modified by the third harmonic waves generated by the mutual interaction of the right and left polarized waves. On the other hand, an elliptically polarized wave shows the nonlinear Faraday rotation whose angle is dependent on the square of the amplitude of an incident wave. Further the inverse Faraday effect is estimated to be proportional to the square of the magnitude of an incident nonlinear circularly polarized wave train. In addition to the present dielectric medium, these phenomena are expected to occur in many systems subject to DNLS equations such as a ferromagnet.