Interaction between ellipse rotation and Faraday rotation in birefringent nonlinear media

Abstract

A lightwave propagating parallel to an applied magnetic field in a dielectric medium will experience a rotation of its plane of polarization by an amount given by θ = VHL. Here V is the Verdet constant, H is the magnetic field strength, and L is the length of the medium. This effect, known as Faraday rotation, is the basis for the operation of magnetooptic current sensors which use optical fibers as the dielectric medium. It is also known through the work of Maker, Terhune, and Savage that an intense elliptically polarized lightwave in a nonlinear dielectric will suffer a rotation of its vibrational ellipse as a result of the intensity-dependent refractive index. Each of these rotatory effects is drastically influenced by the presence of linear birefringence which quenches the rotatory power in the Faraday effect and leads to polarization instabilities in ellipse rotation. In this paper we present a coupled mode theory that yields exact solutions for the interaction between Faraday rotation, ellipse rotation, and linear birefringence in a nonlinear dielectric. The theory shows that competition between the linear and circular birefringences leads to the formation of kink (topological) solitons. One practical result of the theory is that ellipse rotation can be used to enhance the sensitivity of magnetooptic current sensors that rely on Faraday rotation in birefringent fibers.