Spatial Solitons in Modulated Magnetooptic Waveguides

Abstract

The word gyrotropy turns up quite often in physics and it comes from the Greek word gyros, meaning circle [1]. It is used not only in science but in engineering too, as a generic description of an event involving some rotation of the plane of linear polarisation of light. In fact, following Fresnel’s proposition that linearly polarised light is a superposition of two forms of light called left and right-circularly polarised light it is clear that a gyrotropic material is associated with the appearance of elliptically, or circularly, polarised light. It is a very important area that embraces many complex materials which display a wealth of fascinating properties, like optical activity. In general then, a complex relationship exists between the field vectors E and H and the induction vectors D and B, where these quantities have their usual meanings. This relationship can be adjusted to take into account that gyrotropy can be free, natural or forced [1]. Free gyrotropy and forced gyrotropy are in the same category, because ‘forced’ means that it is created by an external magnetic field, for example, and ‘free’ is associated with internal fields. The best known example of natural gyrotropy is optical activity that is exhibited by sugar solutions and this is immediately distinguishable from the forced case by the following signature. Suppose a plane linearly polarised light wave passes once through a natural gyrotropic material causing the plane of polarisation to be rotated. If the same beam is reflected back through the material then, because it has natural gyrotropy, the rotation on the first pass is undone and no final rotation results i.e. no reversal of handedness occurs in this case [2]. This is a very important distinction from forced gyrotropy, which is the property of magnetooptic materials where the rotation of the plane of polarisation would have been doubled. Faraday discovered this and the Faraday effect, as it is now called, involves propagation parallel or antiparallel to an applied magnetic field. Other well-known magnetooptic effects are Voigt and Cotton-Mouton after their discoverers, which occur when the wave propagation is perpendicular to an applied field. Either name can be used but, historically, Voigt dealt with vapours while the second name-pair used liquids. Voigt will be the term adopted here to denote this type of birefringence, which is also revealed by uniaxial crystals, when a wave propagates perpendicular to the optic axis. As will be shown later, for bulk media, the Faraday effect is a non-reciprocal phenomenon and the bulk Voigt [Cotton-Mouton] [1, 2] effect is reciprocal. The really interesting outcome, however, is that even the Voigt effect is non-reciprocal in an asymmetric waveguide.