Dissipative Magneto-Optic Solitons

Abstract

The study of magneto-optics involves the polarization state of light [1,2,3,4], which is a measure of its vector nature. The displacement vector in a magneto-optic medium is D = ε₀ [ε·E + ig ×E], where ε is the relative permittivity that exists in the absence of an applied magnetic field, ε₀ is the permittivity of the free space, g ∝ f(H_app) is called the gyration vector, and the function f (H_app) involves the applied magnetic field H_app. The vector g × E is normal to E and the overall dielectric property tensor of magneto-optic material has off-diagonal elements. For magneto-optic phenomena, as opposed to chiral properties, g Does not depend upon which way the light wave is travelling. This is an important qualification because it means that it continues to act in the same direction, even after the wave has been forced to change direction by a reflection. Hence the physical property described by the form of D is non-reciprocal. A further generalization is that g may depend upon the spatial coordinates. It is common practice to write the displacement vector as D = ε₀ε· E, where ε is now the complete magneto-optic tensor. It is also common practice to write the off-diagonal terms of ε as ±Qn², where n is the refractive index of the un-magnetised dielectric and Qr) is called the magneto-optic parameter distribution. Some common magneto-optic configurations are shown in Fig. 1, in which the direction of the saturation magnetisation M, relative to the propagation direction, is shown.